Universidad de Santiago de Compostela Estimación de las Intensidades de los Núcleos Radioactivos producidos en el Super-FRS en la Futura Instalación del GSI Estimate Of The Intensities Of The Radioactive Nuclides Produced At The Super-FRS At The Future GSI Facility Memoria del Trabajo de Investigación titulado enmarcado en los cursos de doctorado del programa de física de partículas y dinámica no lineal Maria Valentina Ricciardi Junio 2004
Transcript
Universidad de Santiago de Compostela
Estimación de las Intensidades de los Núcleos Radioactivos producidos en el Super-FRS
en la Futura Instalación del GSI
Estimate Of The Intensities Of The Radioactive Nuclides Produced At The Super-FRS
At The Future GSI Facility
Memoria del Trabajo de Investigación titulado enmarcado en los cursos de doctorado del programa de física de partículas y dinámica no lineal
Maria Valentina Ricciardi
Junio 2004
Contents
Introducción (en español) 1
Introduction 3
1 The GSI Future Project 5
1.1 The GSI Future Project 5
1.2 Physical Goals 9
1.2.1 Research with Rare-Isotope Beams – Nuclei far from stability 9
1.2.2 Research with Antiprotons – Hadron Spectroscopy and Hadronic Matter 11
1.2.3 Nucleus-nucleus collisions at high energy – Compressed Nuclear Matter 12
1.2.4 Ion Beam and Laser Beam Induced Plasmas – High Energy Density in Bulk Matter
13
1.2.5 Quantum Electrodynamics, Strong Fields, and Ion-Matter Interactions 14
1.3 Safety Aspects for Design and Operation of the New Facility 14
2 The Superconducting Fragment Separator 17
2.1 Basic principles of the Fragment Separator (FRS) 17
2.2 The Superconducting Fragment Separator (Super-FRS) 23
3 Implementation of the ABRABLA code for the estimation of the RIB
intensities at the Super-FRS entrance
27
3.1 Introduction 27
3.2 The abrasion model in ABRABLA 30
3.3 The ablation model in ABRABLA 32
3.1.1 The evaporation model 32
3.3.2 The fission model 33
I
3.4 The kinematics of the nucleus-nucleus collision 35
3.5 Limitations and applicability of the ABRABLA code for radioprotection purposes
37
4 Results and discussion 40
4.1 Analysis of the data 40
4.2 Results 44
4.3 Discussion 54
Conclusions 63
Conclusión (en español) 65
Bibliography 67
II
Introducción
En febrero del 2003, el gobierno federal alemán aprobó la propuesta para la construcción de
un “Acelerador Internacional para Haces de Iones y Antiprotones”. La futura instalación estará
situada en Darmstadt, Alemania, y representa una extensión del actual laboratorio GSI (Sociedad
para la Investigación de Iones Pesados). La nueva instalación será organizada como un centro de
investigación europeo/internacional, y estructurado como un Grupo Europeo de Interés
Económico (EEIG, European Economical Interest Group).
En los últimos años, un amplio espectro de seminarios, grupos de trabajo, y comités
internacionales han discutido y a la postre puesto las bases para el concepto de la nueva
instalación. La estructura organizativa, el peso de las tareas científicas y el papel de cada
miembro de la organización se discuten actualmente en grupos especializados, de los que la
Universidad de Santiago de Compostela forma parte.
El objetivo principal de la nueva instalación es la construcción de un acelerador técnicamente
innovador y único en el mundo que proveerá un extenso rango de haces de partículas [CDR01].
Se podrá contar con haces de protones y antiprotones y haces de iones de todos los elementos
químicos hasta el uranio, que serán producidos con intensidades inéditas a nivel mundial.
Uno de los principales usos de los haces de iones de alta intensidad es la producción de haces
energéticos de núcleos radioactivos de corta vida, en adelante referidos como Haces de Isótopos
Singulares (RIB, Rare Isotope Beams). Los RIBs se producen en reacciones nucleares sufridas
por los haces primarios de partículas estables. Por esta razón los científicos se refieren a ellos
como haces secundarios. Para conseguir los haces secundarios de la intensidad deseada, la
correspondiente intensidad de los haces primarios tiene que ser adecuadamente alta. El objetivo
tecnológico del futuro sistema de aceleradores es llegar a multiplicar por un factor 100 las
intensidades de los haces primarios respecto a las prestaciones actuales del GSI. Desarrollos
tecnológicos paralelos serán necesarios para proveer detectores y equipo experimental adecuado.
En este contexto el reto más importante es un avanzado sistema experimental que se llama
“Reaction studies with Relativistic Radioactive ion Beams” (R3B) [R3B]. El conjunto
experimental R3B incluye, entre otras cosas, la realización de un espectrómetro magnético
1
superconductor (“Super Fragment Separator, Super-FRS) [SFRS] con una aceptancia mucho
mayor que el actual Fragment Separator (FRS) [FRS], que junta con las altas intensidades de los
haces primarios, permitirán producir haces secundarios radioactivos con intensidades hasta 10000
veces más altas que las que se pueden conseguir hoy en día en el GSI.
Para conseguir las condiciones experimentales óptimas para una cierta investigación
específica, la nueva instalación proveerá energías de haz hasta 15 veces más altas que las
disponibles en el GSI para todos los iones, desde protones hasta uranio.
Obviamente, las altas energías e intensidades de los haces generan un problema desde el punto
de vista ambiental y de seguridad, directamente relacionado con el alto índice de radioactividad
producido. Se requiere una adecuada planificación del blindaje en torno a los aceleradores y áreas
experimentales para asegurar que la radiación producida no escapará del área de confinamiento y
que el nivel de radioactividad fuera de los laboratorios permanecerá por debajo del nivel natural
de fondo.
Los RIBs se producen en reacciones nucleares inducidas por haces primarios de alta
intensidad incidiendo en un blanco localizado a la entrada del Super-FRS. Además del haz
secundario, que será transmitido a través del Super-FRS para su uso científico previsto, se
producirán una gran cantidad de núcleos radioactivos de corta vida. La mayoría de ellos entrarán
en el Super-FRS, serán desviados y abandonarán el Super-FRS lateralmente. Estos núcleos y las
cascadas de neutrones que generarán tienen que ser parados en estructuras blindantes especificas.
Para poder determinar la posición y el espesor de la estructura aislante, es necesario realizar una
estimación fiable de la intensidad de los iones radioactivos producidos en las reacciones
nucleares.
Este Trabajo de Investigación trata del estudio de la producción de núcleos radioactivos y de
su propagación a través de Super-FRS. El medio para realizar el estudio ha sido el código Monte
Carlo ABRABLA de simulación de reacciones nucleares, adecuadamente implementado para el
propósito descrito anteriormente. Este trabajo ofrece una vista general sobre la producción de
radioactividad en el área del Super-FRS, constituyendo el punto de partida para el diseño de la
estructura blindante.
2
Introduction
In February 2003, the German Federal Government approved the proposal for “An
International Accelerator Facility for Beams of Ions and Antiprotons”. The future facility will be
placed in Darmstadt, Germany, and represents an extension of the current GSI Laboratory
(Gesellschaft für Schwerionenforschung). It will be organised as a European/international
research centre, and structured as a European Economical Interest Group (EEIG).
In the last years a broad spectrum of workshops, working groups and international committees
discussed and eventually set the basis of the facility concept. The organisational structure, the
weight of the scientific tasks and the role of each member of the organisation are presently
discussed in international task forces, to which also the Universidad de Santiago de Compostela
takes part.
The principal goal of the new facility is the construction of a worldwide unique and
technically innovative accelerator system that will provide an extensive range of particle beams
[CDR01]. Proton and antiproton beams will be available and ion beams of all chemical elements
up to uranium will be produced with world-record intensities.
The main employ of the high-intensity ion beams is the production of energetic beams of
short-lived (radioactive) nuclei, in the following referred to as exotic or Rare Isotope Beams
(RIBs). RIBs are produced in nuclear reactions experienced by the primary beams of stable
particles. For this reason scientists refer to them as to “secondary beams”. To achieve the desired
intense secondary beams, the primary beam intensities must be correspondingly high. Compared
to the present GSI facility, a factor of 100 in primary beam intensities is the technical goal of the
future system of accelerators. Technical developments are necessary also to provide adequate
detectors and experimental set-ups. In this context, the most challenging item is the advanced
experimental setup for “Reaction studies with Relativistic Radioactive ion Beams” (R3B) [R3B].
The R3B experimental setup includes, among the other tasks, the realization of a super-conducting
magnetic spectrometer (“Super FRagment Separator”, Super-FRS) [SFRS] with much larger
acceptance than the present Fragment Separator (FRS) [FRS]. The large acceptance of the Super-
3
FRS, along with the high primary-beam intensities, would release secondary radioactive-beam
intensities up to a factor 10000 higher than those currently achievable at GSI.
In order to meet the optimum experimental conditions for some specific investigation, the
new facility will also provide beam energies a factor 15 higher than presently available at GSI, for
all ions, from protons to uranium.
Obviously, the high energies and intensities of the beams open up the problem of the
environmental and safety aspects, connected to the high rate of radioactivity produced. Adequate
planning of the shielding around accelerators and experimental areas are required in order to
assure that the produced radiation will not escape the confined area, and the level of radioactivity
outside the laboratories will remain below the natural background level [Fes01].
RIB are produced in nuclear reactions induced by high-intensity primary beams impinging on
a target placed at the entrance of the Super-FRS. Along with the secondary beam, which will be
transmitted through the Super-FRS and then used for the designated scientific purpose, a large
amount of short-lived nuclides (i.e. radioactive nuclei) are produced. Most of them will enter the
Super-FRS, be bent, and then exit the Super-FRS form the sides. These nuclei, and the cascades
of neutrons that they will generate, have to be stopped in devoted shielding structures. In order to
determine the position and the thickness of the shielding, a reliable estimate of the intensities of
the radioactive ions produced in nuclear reactions is needed.
In this “Trabajo de Investigación” we report on the study of the production of radioactive
nuclides and of their propagation through the Super-FRS. The study was performed by means of a
nuclear-reaction Monte-Carlo code, ABRABLA, opportunely implemented for the above-
described purpose. This work offers an overview of the radioactivity production in the Super-FRS
area; the latter is the required starting knowledge for the design of the shielding structure.
4
Chapter 1
The GSI Future Project
1.1 The GSI Future Project
The proposed new facility consists of a 100/200 Tesla⋅meter double-ring synchrotron
(SIS100/200) and a system of associated storage rings for beam collection, cooling, phase-space
optimisation and experimentation (Figure 1.1) [Ang01]. It uses the present accelerators, the
universal linear accelerator UNILAC and the heavy-ion synchrotron SIS18, as injector. Both
synchrotron rings have the same circumference of about 1.1 km and will be installed underground
in the same tunnel at a depth of 24 meters. All the other edifices, housing the Collector Ring
(CR), the New Experimental Storage Ring (NESR), the High-Energy Storage Ring (HESR), the
Super-conducting FRagment Separator (Super-FRS) and the experimental areas, will be build on
ground. On-ground buildings will cover a surface approximately 14 hectare wide.
The project is based on many technological innovations. They will ensure world-unique
characteristics, the most important of which are:
1) Full range of ion-beam species
The system of accelerators will accelerate all ions from protons up to the heaviest element,
uranium. Beams of antiprotons with high intensity will be created from proton beams in the
energy range of 1GeV to 15 GeV.
2) High beam intensities
The 100 Tm synchrotron, SIS100, will produce intense pulsed (1012 ions/pulse) uranium (q =
28+) beams at 1.5 GeV/u and intense pulsed (2.5·1013 ions/pulse) proton beams at 29 GeV. For
the high-intensity proton beams an additional dedicated linac injecting into SIS18 is planned.
3) High beam energies
The 200 Tm synchrotron, SIS200, will provide high-energy ion beams with maximum
energies around 30 GeV/u for Ne10+ beams and close to 23 GeV/u for fully stripped U92+
beams, respectively. The maximum intensities that are possible in this mode are 5⋅1010 ions
per second.
5
Figure 1.1: Present layout of the existing UNILAC/SIS18/ESR facility (blue) and the planned new facilities (red): the Super-conducting Synchrotrons SIS100/200, the Collector Ring CR, the New Experimental Storage Ring NESR, the Super-conducting Fragment Separator Super-FRS, the proton linac, and the High-Energy Storage Ring HESR. The drawing also shows the planned experimental areas for plasma physics, nuclear collisions, rare ion beams, and atomic physics.
6
4) High beam power
Short, high-intensity ion bunches will be available (both heavy-ion and proton beams can be
compressed into 50 ns bunches). Ion pulses with a power of a thousand billion watts can be
generated.
5) Parallel operation
One of the basic advantages of the double-ring concept is its ability to operate in parallel up to
four different beams. This will be achieved by well-coordinated use of the accelerators and
storage rings.
6) Slow extraction
High-energy beams can be extracted over extended periods (order of 10–100 seconds) as an
essentially continuous beam. The slow extraction from the SIS100 is an additional option for
extending the flexibility of parallel operation of experiments.
7) Brilliant beam quality
A collector ring (CR) will be used for stochastic cooling of secondary beams. This will
produce ion and antiproton beams of extreme energy sharpness.
8) Storage rings
The “new experimental storage ring” (NESR) and the “high-energy storage ring” (HESR) will
be used as accumulators and storage rings both for radioactive ions and antiprotons. Both rings
will be equipped with stochastic and electron cooling devices to correct the beam degradation
due to the interaction with the target.
9) Super-conducting Fragment Separator
With the Super-FRS magnetic spectrometer high secondary-beam intensities will be achieved.
It will provide high-luminosity antiproton beams, high-energy proton and ion beams, and short
ion pulses with energies up to 100 kJ.
The technical characteristics listed above will make experimentally accessible a wide
spectrum of scientific scenarios. These are respectively:
1) Multi-disciplinary research
The full range of ion-beam species available at the new facilities will provide a broad basis for
multi-disciplinary research. Investigation of quark matter, of hadronic matter, of hadron
structure, of nuclear structure, of dense plasma, of atomic physics, as well as other
interdisciplinary activities – like material research – will be performed at the new GSI facility.
2) Access to new types of secondary beams
7
Intensities of primary heavy-ion beams will increase by a factor 100. A wide bunch of new
exotic nuclei will be produced and the corresponding secondary exotic beams exploited for the
investigation of nuclear structure, astrophysics and for the study of fundamental interactions.
3) Compressed nuclear matter, charm production and antiproton beams
Nucleus-nucleus collisions at high beam energies will allow producing highly compressed
nuclear matter. Studying highly compressed nuclear matter, physicists can reproduce the
conditions that existed at the birth of the universe. Such extreme forms of matter may also
exist at the centre of neutron stars. Collisions at high energies lead also to a maximum
production rate of hadrons with strange quarks. This enables the study of charm production. At
sufficiently high energies the threshold for the production of antiprotons is overcome. As a
consequence, the production of intense antiproton beams will be possible.
4) Plasma physics experiments
The possibility to compress the ion beam into short bunches is indispensable for plasma-
physics experiments. The knowledge of the behaviour of matter in the high-density plasma
state is essential for inertial confinement fusion, and also for astrophysical studies.
5) Contemporaneity of four different scientific programs
The system of accelerators can operate in parallel up to four different beams. These are for
instance: an antiproton beam, an exotic secondary beam, a high-energy heavy-ion beam
The almost continuous beam – obtainable with the slow-extraction option – maximizes the
luminosity in nucleus-nucleus collision experiments.
7) “Precision” experiments
Precision ion and antiproton beams will be achieved through sophisticated beam-handling
methods, such as stochastic and electron cooling. Together with the statistical precision and
high sensitivity that results from high beam intensities and interaction rates, the sharp-energy
beams will allow to perform “precision” experiments, as for instance to determine the mass of
short-lived, unstable nuclei, or to look for new particles associated with the strong interaction.
8) Mass measurements, electron-nucleus scattering and other research topics
The accelerator rings are unique in their capability to store, cool, bunch, and stretch beams and
thus to fulfil the strict beam phase-space requirements from several experiments. Precision
8
mass measurements, electron-nucleus scattering and other research topics are accessible with
the three rings.
9) Research with high-intensity secondary beams
The Super-FRS magnetic spectrometer will increase up to a factor 10000 the intensity of the
radioactive-beam intensities with respect to the present GSI facility. This will allow to push
the sensitivity of experiments involving short-lived nuclei and antiproton beams, which are the
basis of much of the new research frontiers that will be explored in the new facility.
The facility is expected to serve about 2000 international scientists. About 140 new staff
positions will be created for engineering, on-line testing and project management. The present
estimate of the total cost of the facility is 675 million Euros. The proposed schedule for realizing
the facility extends over 9 years.
1.2 Physical Goals
In this section we will shortly describe the physical goals achievable at the new facility. They
can be sorted into 5 groups.
1.2.1 Research with Rare-Isotope Beams – Nuclei far from stability
The availability of RIBs allows the exploration of the structure and dynamics of complex
nuclei in regions far away from stability. As any other physical system under extreme conditions,
nuclei, pushed to their limits in neutron or proton numbers, reveal new features that lead to new
insights and understanding. The study of nuclei far from stability will permit the study of the
following three areas of investigation [Aum01].
Nuclear-structure studies
On the chart of the nuclides two lines mark the limits of the nuclear existence: the neutron
dripline, beyond which the nucleus decays spontaneously by neutron emission, and the proton
dripline, beyond which the nucleus decays spontaneously by proton emission. The driplines are in
most part still unknown. With RIBs, nuclei at the driplines can be accessed. The structure and
dynamics of such loosely bound nuclei is very different from that of stable nuclei. Rather diffuse
surface zones, so-called halos and skins, were observed in neutron-rich unstable isotopes. Among
other features unique to such exotic nuclei, one expects to encounter novel types of shell
9
structures, new collective modes, new isospin pairing phases, possibly new decay modes, or
regions of nuclei with special deformations and symmetries. Effects of nucleonic clustering
should become more prominent, giving rise to unusual nuclear geometries.
In an atomic nucleus two fundamental forces – the strong and the electroweak interaction –
play a dominant role. The strong force plays the most decisive role. It fundamentally acts between
the quarks, but some of this action leaks out of the nucleon and generates the attractive, short-
ranged nuclear force between the nucleons. This nuclear force is counteracted by the repulsive
electromagnetic force between the protons. The weak force transmutes unstable atomic nuclei
into others and ultimately into stable nuclei. Experimental results on nuclear structure will
provide the adequate benchmark for the nuclear theoretical models, which, in turn, will provide
information on these fundamental forces.
In addition to the exploration of the driplines with exotic nuclei, the production of hypernuclei
– nuclei where some nucleons are replaced by hyperons, nucleons that contain a strange quark –
give access to a new and almost unexplored face of the nucleus. Hyperons are not restricted in the
population of nuclear states as neutrons and protons are. Antiproton beams at the proposed
facility will allow efficient production of hypernuclei with more than one strange hadron. These
exotic nuclei offer a variety of new and exciting perspectives in nuclear spectroscopy and for
studying the forces among hyperons and nucleons.
Nuclear Astrophysics
All atomic nuclei in the universe beyond lithium have been and still are being created in stars.
In various stellar environments this ‘nucleosynthesis’ proceeds via the formation of transient
nuclei that decay into stable ones, either directly or after several intermediate steps. The remnants
of these processes, dispersed from dying stars into the interstellar space, eventually contract and
serve as the seeds for a new generation of stars and their companions, such as our sun and the
earth. Based on key properties of unstable nuclei, nuclear astrophysics is seeking for a reliable
description of the various kinds of stellar nucleosynthesis by which all elements beyond lithium
have been and still are being created. One of its major aims is to understand the abundance of the
elements in the universe. Some of the presumed scenarios of matter creation in stars are: nuclear
fusion, e.g. in the sun; explosive rapid neutron capture (r-process) possibly occurring during the
outbreak of supernovae of type II; rapid proton capture (rp-process) occurring in novae
explosions of accreting white dwarfs, or in X-ray bursts emerging from accreting neutron stars.
The remnants of a supernova might become a fast-rotating neutron star with degenerate, ultra-
10
dense nuclear matter. At present, in particular the explosive nucleosynthesis is to a large extent
not yet understood, due to the lack of appropriate nuclear data.
Fundamental interactions and symmetries
The Standard Model of Elementary Particle Physics summarizes our present knowledge on the
fundamental building blocks of matter – the quarks and the leptons – and their interactions via
exchange particles (so-called gauge bosons). It describes the electromagnetic, the weak and the
strong force, and the fundamental symmetries (or symmetry violations) underlying these forces.
The Standard Model has withstood three decades of extensive experimental scrutiny. Despite its
great success, most physicists are convinced that the Standard Model eventually needs to be
replaced or at least extended. The reason is that it contains disturbingly many parameters whose
numerical values cannot be derived from the theory itself, and also other aspects that seem quite
unnatural. Therefore, many high-energy physics experiments are aimed to search for possible
extensions of the Standard Model. Besides these investigations in particle physics, low-energy
precision experiments in nuclear and atomic physics also show a unique discovery potential for
this field. The major thrust of the nuclear-physics studies focuses on the weak interaction, in
particular on precision experiments of the beta decay of specific exotic nuclei, emphasizing
symmetry violation and the different interaction types of the weak force.
1.2.2 Research with Antiprotons – Hadron Spectroscopy and Hadronic Matter
The basic theory of the strong interaction is the Quantum Chromodynamics (QCD). In the
QCD theory the quarks interact with each other by exchanging particles, the gluons. At short-
distance scales, much shorter than the size of a nucleon (<< 10-15 m), the basic quark-gluon
interaction is sufficiently weak and one can apply perturbation theory, a computational technique
that yields very accurate results when the coupling strength is small. Many processes at high
energies can quantitatively be described by perturbative QCD. The perturbative approach fails
completely when the distance among quarks becomes comparable to the size of the nucleon.
Under these conditions, the force among the quarks becomes so strong that they cannot be further
separated, in contrast to the electromagnetic and gravitational forces, which fall off with
increasing distance. This unusual behavior is related to the self-interaction of gluons: gluons do
not only interact with quarks but also among themselves, leading to the formation of so-called
gluonic flux tubes connecting the quarks. As a consequence, quarks have never been observed as
free particles, they are confined within hadrons, complex particles made of 3 quarks (baryons) or
a quark-antiquark pair (mesons). Baryons and mesons are the relevant degrees of freedom in our
11
environment. An important consequence of the gluon self-interaction is the existence of hadronic
systems consisting only of gluons (glueballs) or bound systems of quark-antiquark pairs and
gluons (hybrids). If the predicted existence of glueballs and hybrids would be proven
experimentally, our understanding of hadronic matter would be strongly corroborated. Along with
this, an important and obscure part of the origin of the universe would be clarified. In fact, in the
evolution of the universe, some microseconds after the big bang, a coalescence of quarks to
hadrons occurred, which was associated with the generation of mass.
In the new facility, the high-intensity antiproton beams will provide access to the heavier
strange and charm quarks and to copious production of gluons. For the testing of the QCD theory
the charmonium spectroscopy, i.e. the spectroscopy of mesons built of charmed quark-antiquark
pairs, is of particular interest.
1.2.3 Nucleus-nucleus collisions at high energy – Compressed Nuclear Matter
In nucleus-nucleus collisions at high energy highly compressed nuclear matter can be formed
for a short time span of less than 10-22 seconds in the collision zone. The compression phase is
followed by an explosive expansion phase where hundreds of particles are emitted. The traces of
these particles can give information on the properties of the nuclear matter. Specifically, the
planned experiments address some of the most fascinating and challenging problems of strong-
interaction physics: the phenomenon of confinement (why are quarks not observed as individual
particles?) and the origin of the mass of hadrons (why is a hadron – that is composed of light
quarks – much heavier than the sum of the masses of its constituents?).
In addition to its relevance for understanding fundamental aspects of the strong interaction,
experiments with heavy-ion collisions can bring information on various, and so far unexplored,
phases of the matter. In the collision, a major fraction of the kinetic energy of the two nuclei is
converted into heat. If the energy pumped in the collision zone is sufficiently large, the hadrons
melt, and the constituents, the quarks and gluons, can move freely forming a new phase, the
quark-gluon-plasma. The temperature at which this deconfinement occurs, i.e. at which hadrons
are expected to dissolve forming quark-gluon plasma, is about 170 MeV. Physicists suspect that
in the early universe, about one millisecond after the Big Bang, such a phase transition occurred
in the opposite direction, i.e. from the quark-gluon plasma into hadronic matter. The phase
transition can occur for different combinations of temperature and density. Of special interest is
also the possible transition at rather low energy but for highly compressed nuclear matter. This
form of matter might exist in the interior of neutron stars.
12
1.2.4 Ion-Beam and Laser-Beam Induced Plasmas – High Energy Density in Bulk Matter
Another research area of the actual and future GSI facility is the electron-ion plasma. In the
electron-ion plasma, the electrostatic forces that bind the electrons with the nuclei are overcome.
This condition is met in a wide range of temperatures and densities. There are indeed numerous
sites in the universe where plasma exists, e.g. at the sun surface, the sun core or the center of
Jupiter.
There are several methods to produce plasma in the laboratory such as electrical discharges in
a gas or laser irradiation of a sample. The use of intense heavy-ion beams is a rather new and
extremely powerful method with unique characteristics. By irradiating a solid-state target,
uniform large-volume plasmas can be produced. At the same time, the ion beams also provide
excellent diagnostic methods to analyse the plasma properties.
A particularly interesting plasma region – the dense, strongly coupled plasma – is located at
relatively low temperature and high density. The interiors of the giant planets Saturn or Jupiter
are interesting examples for this dense plasma region. At the new facility, strongly coupled
plasmas with densities close to those prevailing in the center of Jupiter can be investigated. On
the other hand, the PHELIX laser (Petawatt High-Energy Laser for Ion Experiments), which is
presently being installed at GSI, allows to explore plasmas at higher temperatures, but lower
densities. PHELIX is a laser in the kJ regime with the option to produce ultra-short, high-intensity
light pulses with a total power above 1 PW (1015 W). This laser will be able to produce a light
pressure exceeding the pressure in the interior of the sun.
To create hot and dense plasmas in the laboratory, the combination of these two beams –
pulsed heavy-ion and laser beams – will be used synergistically. This technique will facilitate
novel beam-plasma interaction studies on the structure and properties of matter under extreme
conditions of high energy density, similar to those existing deep inside stellar objects, with keV
temperatures and more than 100 times solid-state density.
Moreover, these studies open up the fascinating possibility of investigating the basic physics
aspects of inertial confinement fusion – for many scientists a process that may represent the future
energy supply for humanity.
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1.2.5 Quantum Electrodynamics, Strong Fields, and Ion-Matter Interactions
In relativistic, high-Z ion-atom collisions, extremely intense photon fields arise due to the high
nuclear charges and to the extremely high velocities. For the heaviest ions, Quantum
Electrodynamics (QED), the ‘standard model’ of electromagnetism and a basis of modern
physics, will be probed near the critical field limit associated with the extreme conditions of high
charge states and high velocities. The fields, present in highly relativistic collisions, are strong
enough to produce particle-antiparticle pairs (e.g. e+e-) directly out of the vacuum.
At high values of the relativistic Lorentz factor the electric and magnetic fields increase
dramatically and are strongly deformed. In contrast to lower energies, where magnetic forces are
generally of minor importance, they start here to equal the electric ones. This high-relativistic
region could not be addressed in any detail up to now. In the new facility, in the strong field limit,
the study of subtle higher-order effects for elementary interaction processes as well as tests of
fundamental symmetries will be experimentally accessible. At the New Experimental Storage
Ring (NESR) the electron-electron interaction will be studied at the new electron target by means
of cooled heavy-ion beams, decelerated in special cases for improved sensitivity.
Finally, we want to quote the applications of the interaction process of relativistic heavy ions
with matter. These are for instance the material research, the biophysics, and the cancer therapy.
In the interaction with biological systems like the cells of human tissue or with electronic
devices like computer memories, heavy charged particles can cause severe damage. In biology,
alterations in the genetic code may cause cancer or long-term mutations. In electronic devices, the
production of locally high ionisation densities and free charges causes single-event upsets or a
local damage in semiconductors. The radiation hardness of electronic modules and satellite
components can be tested with heavy ions before they are launched into space.
1.3 Safety Aspects for Design and Operation of the New Facility
The safety aspects that have to be considered for the design and operation of the new facility
can be divided in two categories: those connected to the ionising radiation produced (radiation
and activation safety) and those connected to the operation and handling of electric and magnetic
devices (industrial safety) [Fes01]. In this section we will speak briefly about the radiation risks
only.
14
Ionising radiations, i.e. beams of particles that, interacting with material, ionise the atoms of
the material, are dangerous for their capability to produce shower of secondary particles –
especially neutrons – that cannot easily be stopped in the vicinity of where they were produced.
Moreover, objects lodged in zones that are regularly exposed to intense flux of neutrons become
active. Figure 1.2 shows the zones where a high level of neutron production and activation is
expected.
The target area of the Super-FRS is among those with higher level of dose rate and activation.
There, beams of heavy nuclei, like uranium, with extremely high intensities, impinge on heavy
production targets, with the consequent generation of a great variety of ionising radiations and a
high flux of neutrons and gamma rays. Therefore, the design of the shielding in the target area of
the Super-FRS has to be studied with great care.
The design of the shielding can be divided in three steps. First, the nuclear reactions occurring
in the collision of the beam with the target have to be modelled with great care in order to
produce reliable quantitative predictions of the produced nuclides (i.e. of the ionising radiations
arising from the collisions) and of their velocities. Then, the kinematical characteristics of the
produced secondary particles have to be used to estimate what is transmitted along the Super-
FRS, what remains in the target area, and what is dispersed at the sides of the SFRS dipoles.
Finally, the dose has to be estimated, i.e. the deposition of energy in the surrounding matter has to
be evaluated from the knowledge of the fluxes of ions. In this “trabajo de investigación” we will
study the first two points. An additional important aspect for the evaluation of the radiation, not
only in the Super-FRS target area but also in zones far from it, is the evaluation of the fluxes of
neutrons produced in the nucleus-nucleus collisions and in the successive interactions of the ions
with the matter. This aspect is investigated with devoted experimental and theoretical studies
[Feh02].
It is important to point out that a reliable estimate of the intensities of the flux of secondary
nuclides impinging on the dipoles of the Super-FRS is of great importance also for the correct
functioning of the machine, since a high level of radiation could cause the quenching (i.e. the stop
of the super-conducting properties) of the super-conducting magnets. In the long term, intense
fluxes of particles are also the reason of the malfunctioning and/or breakdown of the magnets.
The radiation damage that they cause depends not only on the type of particle impinging but also
on its kinetic energy. Therefore, a good knowledge of the kinematical properties of the radiation
produced in the SFRS area is of great importance for the correct running and stability of the
machine. Please note that the contribution of the reaction mechanism to the total kinetic energy is
15
not negligible. For example, the kinetic energy of typical intermediate-mass fission fragments can
differ from the beam kinetic energy of about 200 MeV/nucleon.
Figure 1.2: Overview of the new facility and position of the sites exposed to high neutron flux.
16
Chapter 2
The Superconducting Fragment Separator
In this chapter we want to present some features of the Super-FRS. The following description
is not intended to be neither complete nor technically detailed. We will point out only those
aspects that are relevant for the understanding of the work performed in this “trabajo de
investigación”. In order to point out the basic characteristics of the Super-FRS, we will first
shortly describe how its predecessor, the FRS, works. Therefore, at first we will recall some basic
principles of the functioning of the FRS (section 2.1). Afterwards, in section 2.2, the Super-FRS
will be described.
2.1 Basic principles of the Fragment Separator (FRS)
Selection of a specific exotic beam with the FRS
The FRS is a magnetic spectrometer composed of two sections (see Figure 2.1) separated by a
layer of matter, acting as energy degrader [Gei92]. Each section contains two segments,
composed of one dipole, five quadrupoles and two sextupoles. Before and after the dipole, two or
three quadrupoles with a drift section in between acts as a lens for focalisation. That means that
after focalisation nuclei with the same magnetic rigidities1) but different angles will fall on the
same spot at the exit of the FRS. Sextupoles are used to correct for chromatic aberration, i.e. for
the dependence of the position of the image on the kinetic energy of the particle.
The schematic behaviour of each section can be depicted as in Figure 2.2.
Two groups of particles with two magnetic rigidities, Bρ and Bρ', that leave from point A will
land on different x positions, B and C. The variation in position relative to the variation in
B1) Inside the dipole the magnetic field,r
, is uniform and perpendicular to the velocity, vr
, of the nucleus with charge q and mass m=m0γ. Combining the 2nd law of dynamics and the Lorentz force, the circular trajectory of the nucleus respects the equation:
qp
qv
B =⋅γ
=ρ 0m (2.1)
where ρ is the bending radius of the trajectory, p the momentum of the particle and γ the Lorentz factor. The ratio p/q (= Bρ) is called magnetic rigidity and it is a characteristic of the particle with a certain mass, charge and velocity.
17
magnetic rigidity is a characteristic of the apparatus and it is called “dispersion”1). If in the second
magnet there is the same magnetic field as in the first one, for symmetry reasons two groups of
particles with magnetic rigidities Bρ and Bρ’ that leave from points B and C will land on the
same position A'. In this working condition the spectrometer is therefore “achromatic”. The
achromatism allows the image at the final focal plane to be independent of the momentum spread
of the fragments at the entrance of the system2.
When the beam interacts with the target placed at the entrance, many nuclei are formed.
Among all the produced nuclides we are interested in the selection and transmission of a specific
nuclide, e.g. 132Sn. Due to the physics of the reaction mechanism 132Sn has a certain velocity
distribution, which leads to a corresponding Bρ-distribution. The magnetic fields of the first two
dipoles can be opportunely tuned so that most 132Sn nuclides transverse the FRS on the central
trajectory. The distribution in magnetic rigidity of 132Sn will reflect in a distribution in x-position
in the intermediate plane. Most of the 132Sn nuclides will arrive at the mid-plane (labelled “x1”in
figure 2.2) in the central position, but the distribution will extend also towards B and C. Now,
inserting opportune slits at x1, so that there is a hole in correspondence to the central trajectory,
one can stop particles with Bρ outside a certain range of x-positions, i.e. outside a certain range of
magnetic rigidities. One can decide whether to cover great part of the Bρ-distribution of 132Sn (to
maximise the intensity of the secondary beam) or just the central peak (to filter more). In both
cases, there will be anyhow other fragments, those with magnetic rigidity inside the selected
range, which may pass through the FRS along with 132Sn. Since the magnetic rigidity is a
combination of A, Z and velocity, there is no possibility that the filter at x1 is enough to select 132Sn. For instance, light neutron rich fragments have the same A/Z of 132Sn and similar velocities.
In addition, the velocity distributions of fragments with A/Z quite different from 132Sn can
generate a Bρ-distribution that partially overlap with the Bρ-distribution of 132Sn.
A further selection criterion is needed.
1) The dispersion is defined as:
ρρ=
BdBdxD (2.2)
2 This device was originally introduced [Sim64] as “energy-loss spectrometer”, an apparatus used to study inelastic collisions with electron or ion beams with an energy resolution which is better then the energy spread of the primary beam. The energy-loss spectrometer is basically the scheme of figure 2.2, with the difference that a thin target is placed at the intermediate image plane instead of at the entrance. Some beam particles will interact inelastically, and either the projectile or the target nucleus will end up in an excited state. Since the target is thin and the electronic energy loss of the projectile is small, the system remains substantially achromatic. The x2-position is a measure of the energy lost by the projectile in the collision.
18
Figure 2.1: Schematic drawing of the FRS according to its ion-optic characteristics. Quadrupoles are placed before and after each dipole to define the ion-optic conditions at each image plane. In the middle (dispersive plane), there is an energy degrader.
Figure 2.2: Schematic functioning of the FRS in achromatic mode. Inserting some slits at the mid-plane, one can stop particles with specific magnetic rigidities and let pass only those with a selected magnetic rigidity.
An additional selection can be performed by adding a layer of matter – an energy degrader –in
the mid-plane. If an energy degrader is inserted in the mid-plane, the nuclides will reduce their
velocity according to the energy loss in the matter. Nuclides with higher charge will reduce their
velocity more than the nuclides with smaller charge. The degrader can be opportunely shaped in
such a way that the relative reduction of magnetic rigidity is the same for all the nuclides with a
certain A and Z, e.g. for all 132Sn nuclides, independently of their velocity (i.e. independently of
their position at x1). In this way, most of the 132Sn nuclides will still travel in the central trajectory
also in the second section of the FRS. Other nuclides, with Z close to that of Sn will also reduce
their magnetic rigidity of a percentage close but different to that of Sn. Some of those will also be
19
transmitted through the second section of the FRS. Inserting slits at the final image plane one can
better purify the selected nuclide.
The two selection criteria are met by the fragments lying on the intersection of two lines on
the chart of the nuclides, as for the example shown in figure 2.3 [Sch97]. The position of the first
selection line depends on the magnetic rigidity set in the first section of the FRS. The position of
the second selection line varies with the ratio of the magnetic rigidities of the 1st and 2nd sections
of the FRS and with the thickness of the degrader. Due to the momentum acceptance of the FRS
all the fragments in the overlap zone of the two hatched areas are transmitted. By setting the slits
at the mid- and final planes one can reduce the extension of these areas. With this filtering it is
possible to select a specific secondary beam and suppress most of the unwanted contaminants.
Figure 2.3: Selection criteria, presented in the chart of the nuclides. Full line: first selection obtained tuning (Bρ)1st-section. Dashed line: second selection obtained according to the ratio (Bρ)2nd-section/(Bρ)1st-section and choosing the degrader thickness. Roughly speaking, the first selection is a selection in A/Z and the second one in Z. Setting the slits at the intermediate and final planes one can reduce the hatched areas and in some favourable cases reduce them to a unique fragment (132Sn in the example).
It is clear that a pre-requisite for the correct spatial separation and filtering of the nuclei, both
the beam and the produced nuclides have to be completely ionised, so that their effective nuclear
charge, q, corresponds to their atomic number, Z. The stripping of the electrons occurs in the
passage of the beam/fragments through layers of matter. Depending on the material of the layers
and on the energy of the beam/fragments a certain charge-state population is reached.
To conclude, we want to enumerate here the characteristics necessary to produce secondary
ion beams:
- High intensity of the primary beam. This is essential because most of the desired secondary
beams are beams of exotic (i.e. rare) nuclei, whose production cross section are extremely low
(from nanobarn to picobarn)
20
- High values of the transmission of the device. This is essential for the production of secondary
neutron-rich nuclides originating in fission reactions. This aspect will be discussed again later.
- Selectivity of the apparatus. The ion-optical resolving power has to be high enough to separate
ions of all masses. If the ions are well separated, using the slits at the intermediate and at the
final planes, one can select the desired fragment.
- Sensitivity of the apparatus. There were experiments performed at the FRS where one event
was sufficient to perform the desired investigation (this was the case for instance of a
spectroscopy experiment of 100Sn). Sensitivity, i.e. the capability to select even one single
event, is essential for research with rare isotopes.
The limited acceptance of the FRS
One of the main constrains of the FRS is its limited momentum and angular acceptance.
The momentum acceptance of the FRS is limited to ±1%. This means that if the magnets of
the dipoles are tuned to the magnetic rigidity of 15 T⋅m, then only fragments within 14.85 T⋅m
and 15.15 T⋅m will be transmitted through the FRS. All the other fragments will impinge on the
iron wall of the dipole (see Figure 2.4). The limited momentum acceptance does not affect the
Figure 2.4: Effects of the limited acceptance of the FRS. The beam impinges on the target and many fragments are generated in the nuclear reactions. Due to the high kinetic energy they are all going in forward direction. However, because of the limited angular acceptance many fragments do not enter the 1st dipole and are stopped in the walls of the 1st quadrupole. Due to the limited momentum acceptance, most of the fragments that enter the FRS are bent to the sides and impinge on the iron wall of the dipole. Only those with the selected magnetic rigidity can pass through the FRS.
LEFT
RIGHT
slits
target
quadrupoledipole
Beam
Fragments with large angle
Fragments with small angle
Selected fragment
Fragments with Bρ inside the selected range
Fragments with small Bρ
Fragments with large Bρ
LEFT
RIGHT
slits
target
quadrupoledipole
Beam
Fragments with large angle
Fragments with small angle
Selected fragment
Fragments with Bρ inside the selected range
Fragments with small Bρ
Fragments with large Bρ
21
production of secondary beams (where a Bρ selection is made anyhow). It is not severe even for
other kind of experiments where a complete overview of the production is desired; it is in fact
possible to scan all the magnetic rigidities and then combine the results.
The limited angular acceptance is a bigger constraint. Because of it, not all the fragments that
are produced are transmitted through the FRS. The restrictions brought by the limited angular
acceptance (of about 15 mrad) are better understandable with the help of figure 2.5. The plot of
the velocity of a residue is different depending on the reaction mechanism that produced it. In the
case of fission, the produced nuclide feels the strong Coulomb repulsion of the fission partner.
The magnitude of the velocity is determined basically by the charges of the two fission fragments.
Since the process is isotropic, the resulting velocity is a shell in the centre-of-mass frame. In case
of fragmentation, the Fermi momentum of the nucleons kicked out in the collision and the
evaporation cascade of nucleons from the excited residual nucleus determine the velocity of the
residual nucleus. In this case, the velocity pattern is represented by a full Gaussian distribution in
the centre-of-mass frame. The larger is the number of removed and evaporated nucleons the
larger the width of the Gaussian is. Therefore, for light fragmentation residues the full sphere of
Figure 2.5 can become larger than the cone. The cone represents the limited angular acceptance of
the FRS. What is actually transmitted through the FRS is what lies inside the cone. For heavy
fragmentation products the transmission is about 100%, while for fission fragments it is about
5%.
Figure 2.5: PfragmentationFRS. Only tho
attern of the velocity in the centre-of-mass frame of a certain nuclide produced in or in fission reactions. The cone represents the limited angular acceptance of the se products inside the cone are transmitted.
vlong
C.M. frame vtransv
Laboratory framevtransv
fragmentation
fission
vlong
C.M. frame vtransv
Laboratory framevtransv
fragmentation
fission
22
Originally the FRS was designed for the transmission and separation of heavy fragmentation
residues. However, most neutron-rich exotic ion beams in the intermediate mass region are
accessible preferentially via fission. In order to gain in intensity, the angular acceptance of the
spectrometer has to be increased. This is the main reason why the Super-FRS will be built.
2.2 The Superconducting Fragment Separator (Super-FRS)
In the design of the Super-FRS [Gei03] the phase-space acceptance (i.e. angular and
momentum acceptance) is increased drastically with respect to the FRS. The momentum
acceptance is increased to ±2.5 %, the angular acceptance to 40 mrad in x direction and to 20
mrad in y direction. Though the acceptance is strongly increased, the ion-optical resolving power
is preserved to guarantee the separation quality and the momentum resolution of the spectrometer,
which is essential for the production of exotic nuclear beams. A comparison of the gain factors in
transmission is illustrated in figure 2.6 for uranium fission products as a function of the atomic
number. Of course, the transmission for the very light projectile fragments is also increased
considerably. For example, 19C, produced in the fragmentation of 40Ar at 840 A⋅MeV, whose
transmission is 22 % at the FRS, has a transmission of 71 % at the Super-FRS.
Figure 2.6: Comparison of the values of the transmission for uranium fission fragments with the Super-FRS and the FRS. The gain of pure transmission with the planned Super-FRS in the region of 78Ni is a factor of 30.
The separation method of the Super-FRS is in principle similar to that of the FRS, i.e., a two-
fold magnetic deflection before and after a thick energy degrader. The combination of atomic
energy loss and magnetic deflection provides spatially separated isotopic fragment beams.
23
However, special measures have to be applied due to the high phase-space acceptance and to the
expected high intensity of the projectile beam. The higher phase-space acceptance creates large
optical aberrations. Therefore, sextupole and octupole correction elements have to be
implemented to achieve the necessary separation quality. The high primary-beam intensity leads
to high production rates of parasitic fragments in the degrader, which may have comparable
intensities of those produced at present in the target of the FRS. If these fragments were
transmitted, they would eclipse the desired exotic nuclide. This problem can be solved by
combining two separator stages, a pre-separator and a main-separator (see figure 2.7). Multiple
separation stages are also efficient in reducing the background from the ionic charge states of the
parasitic products.
Figure 2.7 gives an idea on how the Super-FRS works. The system consists of the pre-
separator and the main separator, each equipped with an energy degrader. The pre- and main
separators are independent achromatic systems, so the complete system is also achromatic. The
quadrupole magnets are necessary to provide the ion-optical conditions at the different focal
planes and optimize the operation of the dipole-magnets so to achieve the optimum resolution and
transmission. The sextupole and octupole magnets are used to correct the image aberrations. The
pre-separator (from F0 to F2) acts approximately like the FRS. Fragments are produced in the
target, placed at the entrance (image plane F0). Many of them are deflected by the 1st dipole and
exit the pre-separator. Those with the selected magnetic rigidities pass through and arrive at the
first image plane F1 (first selection of figure 2.3). Due to the large momentum acceptance of the
Super-FRS the amount of fragments arriving at F1 is still large. This can be seen in the first chart
of the nuclides of figure 2.7. By appropriate tuning of the magnetic field of the second dipole and
choosing an appropriate degrader, one can operate the second selection of figure 2.3 (see 2nd chart
of the nuclides of figure 2.7). Using some slits, a bunch of fragments is selected. After the
degrader at F4 there is a reduction in magnetic rigidity that depends mostly on the charge of the
fragments. Seen on the chart of the nuclide, the second part of the separator selects the nuclei of a
transversal band (the almost-horizontal hatched area of figure 2.3). Due to the lower energy of the
fragments after the degrader at F4, the selected band is turned clockwise (see 3rd chart of the
nuclides of figure 2.7). Different fragments follow different paths in the last section of the main
separator. They land at F6 on different positions, and therefore many of them can be stopped in
the slits. Because of the characteristics of the fission process, the band of parasitic fragments at
F1 is quite large compared to fragmentation reactions. As a consequence, also at F6 the number
24
of remaining parasitic fragments is high. The remaining contamination can be eliminated using
event-by-event tracking combined with time-of-flight and energy-loss measurements.
Another difference between the Super-FRS and the FRS concerns the target. The target at
Super-FRS will be loaded with extremely high power, due to the high intensity of the beam. This
requires special construction techniques (e.g., a rotating wheel). However, here we want to
comment only about its thickness. Devoted studies have shown that the optimal target thickness
ranges from few g/cm2 up to 10 g/cm2, depending on the atomic number and on the energy of the
beam. Thick targets bombarded with intense ion beams must face the highly focussed beam and
therefore be able to dissipate large quantities of heat. In this context, it was shown that the most
appropriate target materials are carbon and tantalum. For these reasons, in this work the
calculations will be performed assuming the use of carbon and tantalum thick targets.
An essential input parameter in the calculation is the kinetic energy of the beam. The
conclusion from devoted studies for the optimisation of the working conditions of the Super-FRS
and the experience with FRS experiments show that the Super-FRS should accept beams up to a
maximum magnetic rigidity of 20 Tm corresponding to about 1.5 A GeV 238U92+. This would
represent the limiting case in our simulations.
Finally, we want to point out that the functioning of the Super-FRS requires new and
challenging magnets. The requested large acceptance implies larger apertures of the magnets, and
consequently larger fields. This can be achieved in a cost-effective way using superconducting
magnets. Superconducting magnets are extremely sensitive to radiation. Long-standing radiation
spoils the functioning of the device and has to be estimated for the scheduling of the maintenance
of the facility. The radiation damage depends on the type of particles and on their velocity.
Therefore, the implementation of a computational code capable to correctly estimate the
production of radiation and its kinematical characteristics is essential. A second and more
important aspect is that an intense and localised flux of radiation on the electric wires around the
iron of the superconducting dipoles can cause the quenching of the magnet. Also in this case, the
use of a computational code is essential for the correct design of the device.
25
Figure 2.7: Separation principle of the Super-FRS consisting of the pre- and main-separator stage. In the presented calculated example a 1.5 A GeV 238U primary beam is focused on a 4 g/cm2 carbon target with the goal to provide spatially separated 132Sn isotopes produced in the fission of uranium. The separation performance is illustrated by a presentation of the isotopes transmitted at different focal planes of the Super-FRS. The area of the isotopes in the N-Z plane represents the corresponding intensities resulting from transmission and production probability. The estimated production was calculated with the code MOCADI [Iwa97].
26
Chapter 3
Implementation of the ABRABLA code for the estimation of
the RIB intensities at the Super-FRS entrance
3.1 Introduction
The evaluation of the potential radioactivity in the Super-FRS target area requires employing
computational programs capable to describe the nucleus-nucleus collision at relativistic energies
with high predictive power. Three main types of approaches can be taken: an abrasion-ablation
calculation, a microscopic calculation, and a quantum-mechanical calculation.
Abrasion-ablation statistical models can rather well describe nucleus-nucleus collisions at
relativistic energies. In these models, the nuclei are considered as quasi-classical systems. Their
fermionic nature is taken into account in an approximate way. Microscopic calculations (intra-
nuclear-cascade codes or transport codes) are not suited for radioprotection purposes, since they
take far too much computing time. In addition, their results are not very different from those of
the abrasion-ablation model. More elaborate calculations, using a quantum-mechanic formalism
(e.g. Fermionic nuclear dynamics [Fel00]), are just being developed and not yet applicable to
large systems.
In the following sections, we will describe how the nucleus-nucleus interaction at relativistic
energies is described in ABRABLA [Gai91, Ben98, Dej98, Jun98], the program that was used in
this work to evaluate the intensities of the radioactive residues produced at the Super-FRS
entrance. The ABRABLA code is a Monte-Carlo program that simulates the nucleus-nucleus
collisions at relativistic energies according to an abrasion-ablation model. ABRABLA is
continuously being developed at the GSI since the last 10 years.
The abrasion-ablation model is based on the idea that the nucleus-nucleus interaction can be
schematized by the dynamical picture depicted in figure 3.1.
27
Figure 3.1: Schematic drawing of the nucleus-nucleus collision in the GeV energy regime.
The projectile nucleus and the target nucleus come into contact with some impact parameter.
The two nuclei experience an “abrasion”, in which part of their mass is cut, like with a knife,
according to their volumetric superposition. Only part of the nucleons of target and projectile are
participating to the interaction. They are called “participants” and are filling the horizontal zone
called “fireball” or “firestreak”. The parts of the projectile and target that do not participate to the
interaction are called “projectile-spectator” and “target-spectator”, respectively. The projectile-
spectator and the target-spectator acquire some excitation energy in the interaction. This
excitation energy is consumed by a de-excitation process, called sometimes “ablation”, until the
spectators reach a stable configuration, where they can only decay further by gamma emission.
The de-excitation is described by the statistical model, where the evaporation of nucleons (and
light nuclei, in some cases) and fission are competitive processes. Statistical considerations,
connected to the number of available phase space for the nucleus, rule the probability of
following one or the other channel. With the evaporation of one particle, the nucleus consumes
some energy, but it can still be sufficiently excited to decay, and again fission and evaporation are
competitive decay channels. If the nucleus fissions, the fission fragments usually have some
excitation energy and can evaporate some nucleons.
The kinematical properties of the produced nuclides are very different depending on the
reaction mechanism that generated them. These kinematical properties are not associable to the
mass and charge of the fragment. In fact the same nuclide can be produced in different ways and
arise from the collision with different kinetic energies and angles. For example, the nuclide 42K
can be formed in the reaction 238U+Ti either by fission (figure 3.2 up) or by a long chain of
evaporation of particles (figure 3.2 down). The number of protons and neutrons emitted, their
velocity, their angular distribution, as well as the velocity and angular distribution of 42K are very
different in the two cases. In the first case the Coulomb force between the two fission fragments
confers an additional velocity in any direction of the space (since the process is isotropic). In the
second case the fragment does not strongly modify its original velocity.
28
The nucleons participating to the fireball interact and move on the average in beam direction,
according to a gradient that is zero for the nucleons close to target-spectator (at rest) and close to
the projectile velocity for the nucleons close to projectile-spectator (moving with beam velocity).
In addition, a transversal velocity has to be added, mostly due to the thermal expansion that the
nucleons experience. All the binding energies are overcome, and no structure is preserved, with
the result that all the protons and neutrons of the fireball will move very fast in all the direction of
the space (but not isotropically in the laboratory frame).
evaporation
fragmentation
238U 42K
Ti
238Ufission
evaporation
fragmentation
238U
42K
42K
Ti
238U
Ti
evaporation
fragmentation
238U 42K
Ti
238Ufission
evaporation
fragmentation
238U
42K
42K
Ti
238U
Ti
Figure 3.2: Example of the production of a certain nuclide (e.g. 42K) in the collision of a 238U nucleus with a titanium nucleus. The nuclide can be produced either by fission reaction (up) or by fragmentation reaction (down). We observe the evolution of the 238U-spectator in the reference frame where 238U is at rest.
In this “trabajo de investigación” we implemented the kinematical description of the ions
produced in high-energy nucleus-nucleus collisions in the ABRABLA code, as will be described
in the following sections. The kinematical characteristics of the produced ions are of great
importance to determine what is transmitted along the Super-FRS and what is bent and pushed
aside. This is the basis for the geometrical mapping of the intensity of produced fragments in the
Super-FRS entrance area.
29
3.2 The abrasion model in ABRABLA
In the description of the nucleus-nucleus collisions at relativistic energies, the first step is
treated as an “abrasion” process [Gai91, Bro94]. At relativistic energies the bombarding energy
is well above the Fermi energy. Under this condition, the interaction can be considered an
ensemble of quasi-free nucleon-nucleon collisions. It is assumed that the trajectories of the
interacting nucleons are straight lines and the nucleons participating to the interactions are those
which belong to that part of the nucleus which geometrically overlap with the other nucleus.
Therefore, the masses of the remaining nuclei (both projectile and target spectator) are
determined by the geometrical overlap as function of the impact parameter. For a given projectile-
target combination, the impact parameter determines only the number of removed nucleons from
the initial nucleus, i.e. the abraded mass ∆A, without specifying the proton-to-neutron ratio. The
neutron number and the atomic number of the remaining nuclei are determined just by statistical
consideration. The distribution of the N/Z-ratio after the collision can be calculated applying the
hypergeometrical model. This model assumes that every nucleon removed has a statistical chance
to be a neutron or a proton. This probability can be obtained with the combinatorial calculation.
Assuming that the original nucleus had Zinitial atomic number, Ninitial neutron number, Ainitial mass
number, and that ∆A nucleons were removed, the probability, P(∆Z), that ∆Z protons were
removed is given by:
( )⎟⎟⎠
⎞⎜⎜⎝
⎛∆
⎟⎟⎠
⎞⎜⎜⎝
⎛∆
⋅⎟⎟⎠
⎞⎜⎜⎝
⎛∆
=∆
AA
C
NN
CZ
ZC
ZPinitial
initialinitial
(3.1)
⎟⎟⎠
⎞⎜⎜⎝
⎛kn
C is the binomial coefficient and gives the number of groups that can be formed taking
out k objects of the total n objects. The hypergeometrical model corresponds to the extreme
situation of no correlation at all between the nucleons during the abrasion phase, and results in the
largest width obtainable for the distribution of the proton-to-neutron ratio. This implies that after
the abrasion stage the remaining nucleus is left with a mean N/Z-ratio equal to its original N/Z-
value, although with large statistical fluctuations, which lead to large variations in the N-over-Z
ratio of the reaction products.
30
Before the collision, the nucleons occupying the overlapping volume of the two nuclei are
distributed at random in momentum space inside the Fermi spheres of projectile and target in the
Fermi-gas model (see figure 3.3). As they are removed they leave a “hole” to which is associated
a certain energy. It is assumed that this internal energy of the single nucleons is redistributed
among all the degrees of freedom of the remaining nucleus, which thermalises and forms a
compound nucleus. The total excitation energy induced in the remaining nucleus is given by the
sum of the hole-excitations with respect to the Fermi surface. Again, for statistical considerations,
the mean excitation energy is proportional to the number of nucleons removed, i.e. to the abraded
mass ∆A. It was shown experimentally that for peripheral collisions the mean excitation energy
gained per abraded nucleon is about 27 MeV [Sch93]. However, also the energy induced in the
collision is subject to a large fluctuation and extends to rather high values. Therefore, the
consecutive evaporation cascade has an important influence on the nuclear composition of the
fragmentation products observed.
The same statistical approach is also used to determine the momentum distribution of the
residual nuclei and their angular momentum. The momentum and the angular momentum of the
fragment reflect the Fermi motion of the nucleons in the nucleus, and are directly connected to the
nucleons that are kicked out of the nucleus during the abrasion stage. This part will be described
in more details in section 3.4.
In conclusion, at the end of the abrasion stage, the surviving nucleus is characterised by 5
quantities: the mass, the charge, the excitation energy, the angular momentum, and the linear
momentum. Only the first 4 affect the de-excitation process that will follow, and are used as input
values for the “ablation” stage.
x
y
z
px
py
pz
AB
RA
SIO
N
x
y
z
px
py
pz
AB
RA
SIO
N
x
y
z
px
py
pz
AB
RA
SIO
N
Figure 3.3: Schematic picture demonstrating the action of the abrasion. The abrasion cuts away the nucleons occupying a well-defined area in space (left). These nucleons, however, are randomly distributed in momentum space (centre). As they are removed they leave a “hole” in the nuclear potential well, to which is associate a certain energy (right).
31
3.3 The ablation model in ABRABLA
3.3.1 The evaporation model
At the end of the abrasion stage the residual nucleus is supposed to be left in an equilibrium
state, where the excitation energy acquired with the formation of a limited number of holes is now
redistributed and shared by a large number of nucleons. This equilibrated system, called
“compound nucleus” is characterized by its mass, charge, excitation energy and angular
momentum, with no further memory of the steps that lead to its formation. The momentum of the
nucleus does not affect the deexcitation process.
The excitation energy of the compound nucleus can be higher than the separation energy for
neutrons, protons, alpha or light particles. So, all these particles can be emitted. Protons, neutrons
and alpha constitute the most abundant part of the emitted particles, costing their emission a small
amount of energy (in the order of few MeV). In the version of the ABRABLA code that was used
in this work, the emission of heavier particles is neglected. The emission process can be well
described as an evaporation from a hot system. The treatment starts from the formula of
Weisskopf [Wei37], that is an application of the “detailed-balance principle”, which links the
probabilities Pi→f to go from a condition i to a condition f and vice versa (Pf→i) through the
densities ρi and ρf of the states available in the two systems:
Pi→f ⋅ρi = Pf→i⋅ρf (3.2)
Weisskopf resolved the equation 3.2 for the specific case of particle evaporation. In that
context, Pi→f is the probability to evaporate a particle, i.e. to pass from the initial state of the
compound nucleus (“mother nucleus”) to the final state of the daughter nucleus: Pc→d. The inverse
passage is represented by the fusion of the particle with the daughter nucleus and is ruled by the
inverse cross section σinv – i.e. the cross section for the collision and capture of the particle – and
by the characteristics of the particle. Consequently, the probability to evaporate a particle of type
ν, mass mν, spin Sν⋅ħ, and kinetic energy E is given by:
dE)E(
)EEE(m)S(dE)E(Pc
barsepd
invdc ρ−−ρ
σπ+
= νννν→ 32
12h
(3.3)
where and are the separation energy and an effective Coulomb barrier (that takes into
account tunneling) respectively, and ρ
sepEνbarEν
c and ρd are the level densities of the compound nucleus and
the daughter nucleus, respectively. The total emission width Γν for the particle decay can be
32
found by integrating the equation between zero and the maximum possible eject energy. That
gives:
( ) )EEE(TRm)E()S(E barsep
dc
νννν
ν −−ρρ
+=Γ 2
2
2
π12
h (3.4)
where R denotes the radius of the nucleus, T is the temperature of the residual nucleus after
particle emission. In equation 3.4 was considered that the invariant cross section can be calculated
geometrically knowing the radius of the nucleus. The thermodynamical relation between
temperature and energy was used: E= a⋅T2, where a is the level-density parameter, typically equal
to A/10 MeV (A=mass of the nucleus). In ABRABLA the asymptotic level-density parameter ã,
as given in Ref. [Ign75], was used, that takes into account deviations from non-spherical nuclei.
The density of excited states, ρ, is calculated with the well-known Fermi-gas formula [Hui72]:
454112π
Ea~)Sexp()E( =ρ (3.5)
where S is the entropy calculated as described in reference [Gai91]. In ABRABLA there is no
explicit dependence of the particle decay width on the angular momentum. This is because the
fragmentation process at relativistic energies is expected to populate low angular momentum and
therefore changes in angular momentum along the entire evaporation chain are negligible.
The emission probability of the particle of type ν from the fragment with neutron number N,
atomic number Z, and excitation energy E is given by:
∑ΓΓ
= νν
kk )E,Z,N(
)E,Z,N(W (3.6)
with k denoting all possible decay channels. The decay channels considered in the version of
ABRABLA used in this work are: neutron emission, proton emission, alpha emission and fission.
3.3.2 The fission model
The evaporation process is in competition with another equilibrium process, that is fission. A
fraction of the excitation energy may be spent to induce a collective deformation. As the shape of
the nucleus departs from sphericity, the surface energy increases but the Coulomb energy
decreases. The potential energy reaches a maximum at a deformation stage that is called “saddle
point”. The height of the potential energy over the ground state is the fission barrier Bf. Once a
33
nucleus reaches the saddle point, fission occurs and the nucleus separates into two
complementary fragments.
Also for the fission probability the statistical method introduced before can be applied. Again, the
level densities of the compound nucleus and the exit channel determine the probability. Here the
exit channel is represented by the transition states in the fissioning nucleus in the saddle-point
configuration, because this is a no-way-back configuration. In ABRABLA, the fission-decay
width is calculated according to the transition-state-method of Bohr and Wheeler [Boh39],
reformulated by Moretto [Mor75]:
( ) )EE(T)E(
E fbfissfissc
fiss −ρρ
=Γ2π
1 (3.7)
where ρfiss is the level density of the transition states in the fissioning nucleus in the saddle point,
Efb is the fission barrier and Tfiss the corresponding temperature. The angular-momentum
dependent fission barriers are taken from the finite-range liquid-drop model predictions of Sierk
[Sie86]. In reality, the high excitation-energies induced in the relativistic nucleus-nucleus
collisions performed at the GSI, require a special modeling of the fission decay width, which goes
beyond equation 3.7. In this context, the evolution of the fission, determined by the interaction of
the collective degree of freedom with the heat bath formed by the individual nucleons [Kra40,
Gra83], is followed during the time. This modeling leads to a time-dependent fission width Γf(t).
A dominant parameter is the dissipation coefficient, β, which rules the influence of the nuclear
viscosity on the time needed for the deformation. A comprehensive study and description of this
treatment was recently done in ref. [Jur02].
Once fission occurs, the characteristics of the fission fragments have to be described. This is
done in the fission code PROFI [Ben98], used as subroutine of the ABRABLA code. PROFI is a
semi-empirical Monte-Carlo code developed to calculate the nuclide distributions of fission
fragments. In the model, for a given excitation energy, E*, the yield of the fission fragments with
neutron number N, Y(E*, N), is determined by the number of available transition states above the
potential energy at the fission barrier. It is assumed that the mass-asymmetric degree of freedom
at the fission barrier is on average uniquely related to the neutron number N of the fission
fragments. The number of protons and neutrons are considered to be correlated (although small
fluctuations in the charge density are also introduced in the model). The barrier as function of the
mass asymmetry is defined by three components (or “channels”). The symmetric component,
defined by the liquid-drop potential, is described by a parabola. Two other components, the
34
asymmetric ones, describe the neutron shells at N=82 and around N=88 (known in literature as
“standard I” and “standard II”). They modulate the parabolic potential with four Gaussian
functions. At high excitation energies, the effects of shells are not perceptible anymore, and only
the parabolic potential is reflected in the mass distribution of the fragments. The excitation
energies of the fragments are calculated from the excitation and deformation energy of the
fissioning system at the scission point. A full description of the model is given in [Ben98].
3.4 The kinematics of the nucleus-nucleus collision
Fragmentation residues
Here we will discuss about the momentum distribution of the fragmentation residues in the
context of projectile fragmentation. We will describe facts in the beam reference frame, i.e. in the
frame where the projectile is at rest.
Fragmentation residues are those leftover after the abrasion and the successive chain of
evaporation of particles.
In the frame of the Fermi-gas model, the momenta of the nucleons are distributed in a Fermi
sphere. Their vectorial sum gives the momentum of the nucleus, which is zero in the centre-of-
mass frame. Since the momenta of the ejected nucleons in the abrasion are sampled randomly
from the distribution (see figure 3.3-center), for momentum conservation the surviving spectator
will exhibit a Gaussian momentum distribution. Goldhaber [Gol74] calculated the width of this
distribution and found that it is proportional to the square root of the abraded mass. Crespo et al.
[Cre70] calculated the random combination of small recoil momenta from the sequential
evaporation of nucleons and found that it contributes to the width of the momentum distribution
of the residual fragment by a quantity proportional to the square root of the evaporated mass.
Between the two contributions, the one originating in the abrasion stage is dominant.
Both in the abrasion and in the evaporation processes, the nucleons escaping can occupy any
position in the momentum space. Therefore, the mean value of the distribution does not change,
and the mean velocity of the fragmentation residue is the same as the velocity of the projectile,
i.e. it is zero in the beam frame. In first approximation this conclusion is correct. To a more
correct analysis, the mean velocity of the fragments is not zero, but it is modified in the
component along the beam direction, the “longitudinal” component. The mean velocity of the
fragmentation residues is influenced by two effects. The first effect is a kind of “friction”
35
phenomena that the nucleus experiences during the abrasion with the other nucleus. The net
result, as demonstrated in ref. [Abu76], is a reduction of its longitudinal momentum, which
becomes negative in the beam frame. In ref. [Abu76] it was shown that the reduction of the
longitudinal momentum is proportional to the abraded mass ∆A.
The effect of friction is overcome by another effect that comes into play at smaller impact
parameters. In this case the collision is violent enough to generate a kind of explosion of the
fireball that is in between the two spectators. This explosion causes an acceleration of the two
spectators [Ric03].
In 1989 Morrissey [Mor89] derived semi-empirical parameterisations for the longitudinal
momentum transfer (proportional to the abraded mass, ∆A) and for the width of the Gaussian
distribution (proportional to the square root of the abraded mass, A∆ ). However, the validity of
these parameterisations is restricted to peripheral collisions.
For this reason, we preferred not to use any parameterisation in ABRABLA and we estimated
the momentum distribution of the prefragment after the abrasion, using Goldhaber’s results. The
effects due to friction, fireball blast, and evaporation are neglected because they are of minor
entity.
The program calculates the standard deviation, σ, of the Gaussian momentum distribution of
the prefragment after the abrasion according to Goldhaber’s prescription [Gol74]:
10 −
−⋅σ=σ
proj
prefragprojproj
A)AA(A
(3.8)
where σ0 is given by 5/pFermi and it is approximately around 118 MeV/c for most of the
prefragments. Aproj and Aprefrag indicate the mass of the projectile and that of the prefragment,
respectively. The three components of the momentum of the prefragment are then randomly
sampled from a Gaussian distribution with standard deviation σ and mean value 0. The velocity is
then obtained dividing by the prefragment mass.
As commented above, the evaporation of particles does not affect sensitively the momentum
distribution of the final fragment. However, it is interesting to consider the spectrum of the
evaporated particles. Starting from equation 3.3, assuming the evaporation of a specific type of
particle (e.g. neutrons), assuming that the inverse cross section is constant and introducing some
simplification in the level densities of equation 3.5, one obtains the following energy distribution
for the evaporated particles:
36
dEeEdE)E(P TE
−
ν ⋅≈ (3.9)
from which the evaporative Maxwellian shape of the spectrum is evident. In the program, in each
evaporative step, the energy of the prefragment is reduced by the particle separation energy, by
the Coulomb barrier (when existing) and by the kinetic energy of the particle. The kinetic energy
of the particle is randomly sampled from a Maxwell distribution, as in equation 3.9, defined by
the temperature of the prefragment (the temperature is connected to the excitation energy by: E=
a⋅T2, where a is the level density parameter). A typical value of the kinetic energy for evaporated
neutrons is around 3 MeV, which is quite a low energy. The emission of protons is reduced and
the spectrum is shifted toward higher energies due to the Coulomb barrier.
Fission residues
The kinematics of the fission process is treated inside the program PROFI [|Ben98]. The mean
velocity of fission fragments is estimated by the following empirical description of the total
kinetic energy:
DeZZTKE
221= with d
321Ar
321ArD 231
20131
10 +⎟⎠⎞
⎜⎝⎛ ++⎟
⎠⎞
⎜⎝⎛ +=
ββ (3.10)
where A1, A2, Z1, Z2 denote the mass and charge numbers of a pair of fission fragments prior to
neutron evaporation. D represents the distance between the two charges and is given by the
fragments radii (r0A1/3), corrected for the deformation (β), plus the neck (d). The parameters
(r0=1.16 fm, d=2.0 fm, β1=β2=0.625) were deduced from experimental data in ref. [Böc97] and
are consistent with values previously found in the analysis of ref. [Wil76]. At low energies, the
dependence of the β parameters on the fission channel is considered. When the momentum
conservation is imposed to the reaction, the velocities of the two fission fragments are
determined.
3.5 Limitations and applicability of the ABRABLA code for radioprotection purposes
The output information given by ABRABLA after the implementation performed in this work
is the Z, A and velocity of the residues from the projectile. This is sufficient to have a mapping of
37
the intensities of the secondary nuclei produced in the Super-FRS target area, which is the
purpose of this work.
However, the modeling of the nucleus-nucleus collision realized in ABRABLA has some
limitations, connected to the approximations used in the descriptions of the physical processes.
The use of the code is therefore limited by the following conditions:
- target and projectile must have mass larger than 10
- the beam kinetic energy should be larger than about 100 MeV per nucleon
- the total energy of the system in the center of mass should be much larger than the sum of
the binding energies of projectile and target
These limitations do not touch the cases studied here, which concerns heavy-ion interactions at
relativistic energies.
A quite important restriction of the applicability of the ABRABLA code for radioprotection
purposes is that its predictive power is limited to fragments above Z ≅ 10. While the production
of intermediate and heavy fragments can be successfully performed with the evaporation-fission
mechanisms, as described in ABRABLA, most of the light fragments are produced with another
reaction mechanisms: multifragmentation. Multifragmentation takes place when not-peripheral
collisions occur. In these events, the simultaneous formation of several light (Z<10) fragments is
occurring: the “multiplicity” – i.e. the number of produced fragments per event – is bigger than
one. Although the probability that multifragmentation events occur is rather low, the high
multiplicity contributes to increase noteworthy the intensity of the very light fragments. We will
comment on this restriction in the next chapter.
Another restriction is that the model describes only the nucleus-nucleus interaction itself, i.e.
the code works only for thin targets. In the calculations performed in this work, thick target were
assumed. This introduces an error, which will be discussed in the next chapter.
A more detailed mapping of the radioactivity building up in the new facility requires
information not fully provided by ABRABLA. These are for instance the neutron production in
the reaction and their transport through the matter (with consequent secondary reactions) and the
secondary reactions of the fragments in thick targets, which produce additional amounts of
neutrons. The knowledge of the fluxes of neutrons produced in the new facility is a particularly
important issue because it affects the planning for the construction of the shielding. Obviously, a
comprehensive transport code would be more appropriate for this purpose. However, most of the
transport codes for nuclear reactions do not treat nucleus–nucleus collisions, at least not for
38
medium-mass and heavy nuclei. Monte-Carlo codes as LAHET-MCNPX [LCS] are indeed more
suited for the calculation of neutron fluxes in complex geometry, but, unfortunately, they only
treat the case of nucleon-nucleus collisions. Recently, nucleus-nucleus collisions were
implemented in FLUKA [FLU], GEANT [GEA] and SHIELD [SHI], but still the accuracy of the
results have to be benchmarked. In fact, these transport codes suffer of some deficiencies, which
reduce the accuracy of the result. Specifically, these codes were developed for the simulation of
other physical cases, like high-energy particle interactions or low-energy neutron interactions.
The treatment of the heavy-nuclei collision at energies around 1 GeV/nucleon is in some cases
fragmentary. This is for instance the case of the fission mechanism, which is often parameterized.
The consequence is that the predictive power for the production yield of the residual nuclei is
often scarce. On the other hand, the total reaction rate and the evaluation of the neutron fluxes
and angular distributions are rather realistic.
For the design of the shielding around the Super-FRS and for the handling of the Super-FRS
itself, a good knowledge of the secondary beam production is essential. In fact, if the A/Z of the
most produced isotopes is wrongly estimated, due to the bending occurring inside the dipoles,
also the radiation arriving at the iron walls of the spectrometers is wrongly estimated.
A correct mapping of the secondary beams impinging on the iron walls of the dipoles and on
the concrete shielding relies upon an accurate estimate of the yield of residues and on their
velocity. This justifies the work performed with ABRABLA. ABRABLA was extensively
benchmarked and its predictive power widely tested. It provides results that are in excellent
agreement with the experimental data. For many reactions, the formation cross sections of the
most produced isotopes are predicted with few percent relative error, and the most exotic nuclei
with few tens of percent of relative error. The other codes available are often off of even 3 orders
of magnitude.
39
Chapter 4
Results and discussion
Once the production of the fragments is simulated with ABRABLA and the production cross
sections estimated, the transport of the fragments along the Super-FRS has to be done. To this
purpose we wrote an analysis program. The program was written in PL/I [PLI]. The SATAN
[SAT] graphic package was used to set the gate conditions and for the graphic presentations.
4.1 Analysis of the data
The analysis program
The output of the ABRABLA simulation gives event-by-event the following quantities:
- the mass number of the final fragment
- the atomic number of the final fragment
- the x, y, and z components of the velocity of the fragment in the beam frame
and other additional information like the impact parameter, the number of abraded neutrons and
protons, the number of evaporated neutrons, protons and alpha particles, the type of reaction
(nuclear reaction without fission; electromagnetic excitation – i.e. coulomb interaction without
collision – without fission; electromagnetic excitation with fission; nuclear reaction with fission),
the energy of the prefragment after abrasion, the energy at fission (above the fission barrier).
The three quantities listed above are those used to draw the map of the produced nuclides in
the Super-FRS target area.
The simulation gives the results for a nucleus-nucleus collision, i.e. for the case of an
infinitely thin target. The feasible experimental cases for the future Super-FRS facility assume the
use of rather thick production targets. In addition to the target, another layer of matter, the
stripping foil, has to be traversed by beam and fragments. The passage through these two layers
of matter has two consequences: the first is that both the beam and the fragments experience some
energy loss and consequently reduce their velocity; the second is that the fragments themselves
can interact with the target/stripper nuclei, i.e. perform secondary reactions. In this analysis we
40
will take into account only the first case and neglect the second one. The first case has to be
considered because a correct evaluation of the velocity of the beam/fragment is essential for the
correct knowledge of its magnetic rigidity, and, consequently, of its bending inside the dipoles of
the spectrometer. Therefore, for a reliable mapping of the intensities of the nuclides produced, a
correct knowledge of the velocity is essential. On the contrary, secondary reactions can be
ignored. In fact their effect is to reduce the production of a given nuclide of a few percent, and
increase the production of other nuclides. A variation of a few percent does not change the order
of magnitude of the intensities, whose knowledge is the purpose of this work.
Let us consider how the reduction of velocity occurs. A beam exits from the synchrotron with
the energy per nucleon of 1.5 GeV, corresponding to the velocity in the laboratory frame
υbeam-init = 26.69 cm/ns. The energy in the synchrotron, measured by determining the revolution
frequency, is taken as a reference. The velocity of the reaction products in the laboratory frame
has to be calculated considering three contributions:
1) The energy loss of the beam. Before the nuclear reaction occurs, the beam transverses some
layers and part of the target and reduces its energy because of Coulomb interactions with the
electrons of these materials. So at the moment of the reaction, the velocity of the beam
– υbeam-react – is reduced with respect to the initial one. The value of υbeam-react is calculated with
the following passages: 1) the range of the beam in the target is calculated considering the
initial beam energy, its mass, its charge and the mass and charge of the target; 2) the position
(depth) in the target at which the reaction occurs is chosen randomly (with equal probability
for every point) and the thickness of the two sections1 of the target is calculated; to these
thickness correspond a range; 3) the range of the beam is reduced by the thickness of the first
section of the target; 4) the reduced range of the beam is transformed back into energy and the
energy into the velocity in the laboratory frame. All these passages were performed using
some procedures taken from ref. [Röh94].
2) The nuclear reaction releases a certain velocity to the fragment. This velocity is the output
data of ABRABLA, given in the beam frame. It is transformed into the laboratory-frame
velocity by means of the Lorentz transformations:
creactbeam−υ−
=β (4.1)
1 The sections behind and beyond the point where the reaction occurs.
41
2
2
1
1
cz
xlabx βυ
−
β−⋅υ=υ
2
2
1
1
cz
ylaby βυ
−
β−⋅υ=υ
21c
z
reactbeamzlabx βυ
−
υ+υ=υ − (4.2)
where –υbeam-react is the velocity with which the laboratory frame is moving with respect to the
beam frame, c is the velocity of the light, υx, υy, υz, are the components of the velocity of the
fragments in the beam frame, and , , are the components of the velocity of the
fragments in the laboratory frame. The component along the beam direction is conventionally
the z-axis. Please note that the relative velocity between the two systems is υ
labxυ
labyυ
labzυ
beam-react.
3) Finally, the fragment has to transverse part of the target and the stripper, depositing in them
some energy and reducing consequently its velocity. Again, to calculate the reduction of its
velocity the following passages are done: 1) the energy of the fragment is calculated from its
velocity; 2) the range of the fragment in the target is calculated considering its energy, its
mass, its charge and the mass and charge of the target; 3) the range of the fragment is reduced
by the thickness of the second section of the target; 4) points 2 and 3 are redone for the case of
the stripper; 5) the reduced range of the fragment is transformed back into energy and the
energy into the velocity in the laboratory frame. We label this velocity with ,
, . All these passages were performed again using the procedures taken from ref.
[Röh94].
labxυ
labyυ
reducedlabz
−υ
The velocity with which the two reference frames are moving is calculated considering the
point where the fragment is generated, i.e., where the nuclear reaction occurs. The production of
fragments in the stripping foil is neglected because the mass of the foil is about 2% the mass of
the target.
Having done the procedures described above, we have the velocity of the fragment in the
laboratory frame after the passages through the layers of matter. Please note that we assume that
the passage through the matter, and the consequent energy loss ∆E, changes the Bρ of the
fragment but does not affect the angle θ. With this information we can calculate the orthogonal
velocity , the angle θ, and the magnetic rigidity Bρ of the fragment: lab⊥υ
42
( ) ( )22 laby
labx
lab υ+υ=υ⊥ (4.3)
⎟⎟⎠
⎞⎜⎜⎝
⎛
υυ
=θ −⊥reducedlab
z
lab
tana (4.4)
cZA
euB βγ=ρ (4.5)
where A is the mass number, Z is the atomic number, u is the atomic mass unit, -e is the electron
charge, γ = (1 - β2)-½.
Analysis of the results
Making this procedure for every event, the spectra presented in figure 4.1 could be filled.
Figure 4.1-left presents the acceptance plot of all fragments produced in some nuclear reaction (in
the example, a 238U beam at 1.5 GeV per nucleon impinging on an infinitely thin tantalum target).
This two-dimensional spectrum collects the number of fragments (coloured pixels) having a
certain magnetic rigidity (x-axis) and produced with a certain angle (y-axis). In this plot, the
position of the beam is represented by a spot, whose coordinates are x = 16.64 (its beam magnetic
rigidity after the passage through target and stripper foil) and y = 0 (its angular spread is
negligible). Figure 4.1-right presents the acceptance plot of one specific nuclide produced in the
same nuclear reaction (in the example, 132Sn). In both figures three lines are overlaid. The
horizontal line at y=30 marks the limit of the angular acceptance of the Super-FRS (average value
between x and y). What falls above this line will impinge on the entrance quadrupole. The two
vertical lines at x=17.35 and x=18.24 represent the lower and upper acceptance limit for the
magnetic rigidity of the Super-FRS tuned in order to transmit the nuclide 132Sn. What falls inside
the narrow rectangle is transmitted; what falls outside will impinge on the iron walls of the first
dipole. Specifically, ions with magnetic rigidity above 18.24 Tm will be less bent and impinge on
the right wall of the dipole2; those with Bρ<17.35 Tm will be more bent and impinge on the left
wall of the dipole. Also the beam will impinge on the left wall of the dipole.
Thus, the procedure for the analysis of the data is straightforward. The acceptance plot of the
selected fragment is used to determine the Bρ-window, represented by the narrow rectangle,
which gives the limits in magnetic rigidity of the fragments transmitted along the Super-FRS. The
window is determined considering that for a give value of the magnetic field the spectrometer has
2 See figure 2.4 for convention on “right” and “left”.
43
a limitation in magnetic rigidity of ±2.5%. The position of the window is chosen in order to
maximise the counts of the selected fragment inside of it. Once the window is placed, the gating
conditions are set, and the events falling inside the four rectangular areas delimited by the three
lines can be analysed separately.
Figure 4.1: Acceptance plot of all fragments (left) and of a specific one (right), 132Sn. In the example, the reaction 1.5 A GeV 238U beam on tantalum is presented. The beam is represented by the spot at x = 16.64. The horizontal line at y=30 marks the limit of the angular acceptance of the Super-FRS. Events falling inside the narrow rectangle represent ions that are transmitted along the Super-FRS; what falls outside impinges on the iron walls of the first dipole.
4.2 Results
After impinging in the target and in the stripping foil, the intensity of the beam is reduced.
Nevertheless the intensity of the surviving beam that enters the 1st dipole is still high and
concentrated in a specific spot. This requires a devoted shielding. In order to scan the
distributions of intensities of surviving beams and fragments, we analysed three extreme cases:
1) Selection of a fragment with Bρ close to the Bρ of the beam. In this case the surviving
beam has to be stopped in some slits.
2) Selection of a neutron-rich fragment. In this case the surviving beam will stop in the iron
of the 1st dipole, on the right wall
3) Selection of a proton-rich fragment. In this case the surviving beam will stop in the iron
of the 1st dipole, on the left wall
44
As pointed out in section 2.2, for the production of exotic beams the target will be loaded with
extremely high power. This reduces the possibilities on the choice of the target to two materials:
tantalum and carbon. The study of the target thickness was performed at the Super-FRS group at
GSI [Wei04]. The thickness of the target was chosen using the program LISE [Baz02], which
calculates the transmission through the Super-FRS of the selected nuclide for different target
widths and chose the thickness corresponding to the maximum intensity at the exit.
Selection of a fragment with Bρ close to the Bρ of the beam
We choose the case of a 238U beam on a tantalum target, at 1.5 GeV/nucleon, with a primary-
beam intensity of 1·1012 ions/s. The target is 5.225 g/cm2 thick, corresponding to 20% of the
range of the projectile. The fragment selected is 130Sn.
ABRABLA gives us the values of the cross sections for nuclear reactions and for
electromagnetic interactions: σnr = 7.5908 b, σem = 5.2710 b. The percentage of electromagnetic
interactions and of nuclear reactions occurring in the target and the total number of beam particle
consumed can be calculated3 and are: pem = 8.2 %, pnr = 11.8%, preac = 20.0%. That is to say:
2.0·1011 beam-particles/s are consumed and 8.0·1011 beam-particles/s survive. Among these
2.0·1011 interactions/s 20.6 % of interactions lead to total disintegration of the nucleus, and 79.4
% of interactions lead to the formation of residues (60.0 % of fragmentation reactions and 19.4 %
of fission reactions). Fragmentation reactions contribute with one fragment, fission reactions with
two. Thus the intensity of the fragments produced in the reactions is 2.79·1011 ions/s. The
distribution of the produced fragments, presented in the chart of the nuclides, is reported in figure
3 The attenuation of the beam in the matter of thickness x is given by the formula: ( )xkxk
where k contains the Avogardo's number NA, the target mass MT and density ρT:
T
TA
MN
kρ⋅
= (4.7)
The percentage of nuclear reactions and electromagnetic interactions are given by:
emnr
nrreacnr pp
σσσ+
⋅= and emnr
emreacem pp
σσσ+
⋅= (4.8)
45
4.2. The distribution is normalised to the intensity (2.79·1011). The most produced fragments are 236U and 237U. They have a velocity approximately equal to that of the beam and not much spread.
This means that they also will produce a well-localised spot of intensity in some point of the
dipole wall.
In figure 4.3-left the acceptance plot of all fragments is presented. The plot is normalised to
2.79·1011, which corresponds to the intensity of the produced fragments. The sum of the events
falling above the horizontal line at y=30 gives the intensity of the fragments stopped in the
quadrupole: 7·106 ions/s. The intensity of the fragments entering into the 1st dipole of the
spectrometer is: (2.79·1011 - 7·106) ions/s ≅ 2.79·1011 ions/s.
In figure 4.3-right the acceptance plot of the selected fragments is presented. The plot is
normalised to 2.46·108, which corresponds to the intensity of 130Sn. The gate plotted in the figure
represents the best choice for the tuning of the spectrometer in order to transmit the maximum
possible intensity of 130Sn. The width of the window is determined by the constraint in magnetic
rigidity, limited to ±2.5% in the future Super-FRS. Once the gate is established in figure 4.3-right,
the same window is imposed in the full acceptance plot of figure 4.3-left. The three windows
below the limit of y=30 mrad give the intensity of the fragments falling on the left iron wall of the
1st dipole, the intensity of the fragments transmitted, and the intensity of the fragments falling on
the right iron wall of the 1st dipole, respectively. Numerically we have: fragments going in the left
iron wall of the dipole (surviving beam excluded): 2.04·1011 ions/s; fragments going in the right
iron wall of the dipole: 2.4·1010 ions/s; fragments transmitted: 5.1·1010 ions/s. The black spot in
figure 4.3-right at x=16.64 represents the surviving beam. In order to avoid the transmission of
the surviving beam, slits have to be placed after the first dipole. The slit on the left side is
represented in figure 4.3-left by the vertical black thick line. So, the slit gets the intensity of
8.0·1011 ions/s in one localised spot, plus a minor contribution of fragments with the same
magnetic rigidity of the beam.
Figure 4.4 depicts the distribution of the fragments stopping in the dipole walls, represented in
the chart of the nuclides. In figure 4.5 the nuclides impinging on the dipole walls are presented
integrated over the atomic number, versus their velocity. These plots are important to have an
idea of the possible radiation damage of the superconducting magnets. Finally, in figure 4.6, we
present a contour plot of the radii of the trajectories of the fragments, entering the 1st dipole of the
Super-FRS, tuned to transmit the selected fragment (130Sn). The central trajectory has a radius of
12.5 meters.
46
All the numerical results are collected in table 4.1. Table 4.2 collects also all other possibilities
of different tuning of the magnets. The magnetic rigidity is scaled in steps of 5%.
In section 3.5, we commented that the yields of fragments below Z ≅ 10 is underestimated.
Light fragments are produced in multifragmentation events with high multiplicity, which is not
taken into account in ABRABLA. These very light fragments are characterized by a large
spectrum of velocities. The experience with experiments performed with full-acceptance
spectrometers (see for instance ref. [Sch96]) in the 1GeV region shows that their velocity can
vary between 0 and 4 cm/ns in the centre of mass. Since the velocity originates mostly in the
abrasion process, we can safely assume that the range of velocities remains practically the same
also for 1.5 GeV beam energy. Applying this to our case, we would obtain that their magnetic
rigidity can vary between 12 Tm to 19 Tm. As a consequence, the higher intensity of these
fragments has to be distributed among a large spectrum of magnetic rigidities, i.e. of trajectories.
This makes the flux rather low. Therefore, as a first estimation of the yields – that is the purpose
of this work – light fragments are neglected. Also, the flux of neutrons arising in central
collisions, leading to the full disintegration of the nuclei, is neglected. Devoted studies,
experimental and theoretical, are being performed separately [Feh02].
Figure 4.2: Distribution of produced fragments in the reaction 238U on tantalum, presented in the chart of the nuclides. The beam has an initial energy of 1.5 GeV per nucleon, and intensity 1·1012 particle per second. The coloured scale gives the intensity in ions/second.
47
Figure 4.3: Acceptance plot of all fragments (left) and of the selected one (right), 130Sn, for the reaction 1.5 A GeV 238U beam on tantalum. The horizontal line at y=30 marks the limit of the angular acceptance of the Super-FRS. Events falling inside the narrow rectangle represent ions that are transmitted along the Super-FRS; what falls outside impinge on the iron walls of the first dipole. The beam is represented by the spot at x = 16.64. What falls on the black vertical line at x = 16.64 is stopped in the slits. The coloured scales give the intensity in ions/second.
Figure 4.4: Distributions of fragments stopped in the iron walls of the 1st dipole. The coloured scale gives the intensity in ions/second.
Figure 4.5: Distributions of velocities of the fragments stopped in the iron walls of the 1st dipole. The coloured scale gives the intensity in ions/second.
48
Figure 4.6: Distribution of the radii of the trajectories of fragments produced in the reactions, when the magnetic field is tuned to transmit 130Sn. The coloured scale gives the intensity in ions/second.
Selection of a neutron-rich fragment
We choose the case of a 48Ca beam on carbon target, at 1.5 GeV/nucleon, with a primary-
beam intensity of 1·1012 ions/s. The target is 6 g/cm2 thick, corresponding to about 14% of the
range. The selected fragment is 11Li.
The results given by the simulation performed with ABRABLA were analysed as described
for the previous case. In figure 4.7 the production of nuclides is presented on the chart of the
nuclides. Please note that in this case great part of the products is constituted of light masses. In
this case the use of the abrasion-evaporation code is in principle inappropriate. In fact, many
collisions introduce enough energy to induce the multifragmentation of the nucleus. In order to
improve the prediction of the ABRABLA code for this case, we introduced an intermediate
reaction step in-between abrasion and evaporation that depicts the “break-up” of the nucleus into
several fragments. This intermediate stage, was introduced as a simple parameterisation deduced
from experimental data. The study and parameterisation of the break-up stage was performed in a
previous work [Sch02]. The parameterisation of ref. [Sch02] takes into account the consumption
of energy burned up in the multifragmentation of the nucleus, but does not follow explicitly the
history of all the fragments formed at once in the process. In every event, the successive
deexcitation of only one fragment formed in the break-up is performed. Although the introduction
of the break-up stage improves considerably the prediction (see ref. [Sch02]), results for
fragments with Z ≤ 4 are underestimated, since the production of protons, alphas and light
nuclides is dominated by the evaporation and by multifragmentation events with high
multiplicity. Devoted studies that consider the products of the evaporation and of the total
49
disassembly of the nucleus have to be performed. On the other hand, we must consider that the
most dangerous residual nuclei, both in terms of radioactivity and of radiation damage, are the
heavier fragments. So the results presented here are indeed of great interest for the safety issue.
The selected fragment (11Li) has such a low formation cross-section that the simulation of its
production with sufficiently high statistic would require a long computing time. In order to
bypass this difficulty we have reproduced the magnetic rigidity of 11Li exploiting the velocity
distribution of 9Li. This is justified by the fact that all the lithium isotopes are produced with the
same reaction mechanisms (fragmentation). As explained in section 3.2, the formation of
fragments with similar mass is expected to lead to similar velocities. The scattered plot of the
magnetic rigidity of 11Li is used only to set the gate that defines the transmitted fragments (see
figure 4.8). The magnetic rigidity of 11Li is so high (due to the high value of A/Z) that the bulk of
the production has a lower Bρ and falls consequently on the left wall of the 1st dipole. Therefore,
the distribution of fragments impinging on the right iron wall of the first dipole is equivalent to
the whole production presented in figure 4.7. The velocity distribution of fragments impinging on
the right iron wall of the first dipole is presented in figure 4.9. In figure 4.10 the distribution of
the radii of the trajectories of the produced fragments is depicted.
The numerical results are collected in Table 4.3. Table 4.4 collects all other possibilities of
different tuning of the magnets. The magnetic rigidity is scaled in steps of 5%.
Figure 4.7: Distribution of pro-duced fragments in the reaction 48Ca on carbon, presented on the chart of the nuclides. The beam has an initial energy of 1.5 GeV per nucleon, and intensity 1·1012 particles per second. The coloured scale gives the intensity in ions/second.
50
Figure 4.8: Left: Acceptance plot of all fragments for the reaction 1.5 A GeV 48Ca beam on carbon. The coloured scale gives the intensity in ions/second. The horizontal line at y=30 marks the limit of the angular acceptance of the Super-FRS. The few events falling inside the narrow rectangle represent ions that are transmitted along the Super-FRS; what falls outside impinges on the iron walls of the first dipole. The beam is represented by the spot at x = 17.20. Right: Acceptance of the selected fragment, 11Li. The plot was constructed using the angular and velocity distributions of 9Li. The coloured scale gives the intensity in arbitrary units.
Figure 4.9: Distributions of velocities of the fragments stopped in the left iron wall of the 1st dipole. The coloured scale gives the intensity in ions/second.
Figure 4.10: Distribution of the radii of the trajectories of fragments produced in the reactions, when the magnetic field is tuned to transmit 11Li.
51
Selection of a proton-rich fragment
We choose the case of a 238U beam on carbon target, at 1.5 GeV/nucleon, with a primary beam
intensity of 1·1012 ions/s. The target is 4 g/cm2 thick, corresponding to about 10% of the range. The
selected fragment is 100Sn.
The production of nuclides given by the simulation performed with ABRABLA is presented in the
chart of the nuclides in figure 4.11. The data were analysed as described previously. Please note that the
nuclides with highest production are 237U and 236U. They have a rather narrow velocity distribution and
consequently their magnetic rigidity will be concentrated in a short range of values.
As in the previous case, here the selected fragment (100Sn) has such a low formation cross-section
that the simulation of its production with sufficiently high statistic would require a too long computing
time. Therefore, we have reproduced the magnetic rigidity of 100Sn exploiting the velocity distribution
of a close tin isotope. In fact, close isotopes are produced with the same reaction mechanisms – again
fragmentation – and have therefore similar velocities. This assumption was verified by checking the
spectra of the isotopes close to 100Sn. Neutron-rich isotopes were excluded because they are produced in
fission reactions. The scatter plot of the magnetic rigidity of 100Sn is used only to set the gate that
defines the transmitted fragments (see figure 4.12). In contrast to the case of the neutron-rich 11Li,
whose magnetic rigidity is very high, the magnetic rigidity of the proton-rich 100Sn is not particularly
low; for example, it is similar to that of many light fragments, which have the same A/Z ratio.
We present the distribution of fragments impinging on the right and left iron walls of the first dipole
in figure 4.13, and their velocity, in figure 4.14. In figure 4.15 the distribution of the radii of the
trajectories of the produced fragments is depicted.
The numerical results are collected in Table 4.5. Table 4.6 collects all other possibilities of different
tuning of the magnets. The magnetic rigidity is scaled in steps of 5%.
Figure 4.11: Distribution of produced fragments in the reaction 238U on carbon, presented on the chart of the nuclides. The beam has an initial energy of 1.5 GeV per nucleon, and intensity 1·1012 particles per second.
52
Figure 4.12: Left: Acceptance plot of all fragments for the reaction 1.5 A GeV 238U beam on carbon. The coloured scale gives the intensity in ions/second. The horizontal line at y=30 marks the limit of the angular acceptance of the Super-FRS. Events falling inside the narrow rectangle represent ions that are transmitted along the Super-FRS; what falls outside impinge on the iron walls of the first dipole. The beam is represented by the spot at x = 16.64. Right: Acceptance of the selected fragment, 100Sn. The plot was constructed using the angular and velocity distributions of close tin isotopes. The coloured scale gives the intensity in arbitrary units.
Figure 4.13: Distributions of fragments stopped in the iron walls of the 1st dipole.
Figure 4.14: Distributions of velocities of the fragments stopped in the iron walls of the 1st dipole.
53
Figure 4.15: Distribution of the radii of the trajectories of fragments produced in the reactions, when the magnetic field is tuned to transmit 100Sn.
4.3 Discussion
The starting results of this work are the map of the residual nuclides produced at the Super-FRS and
their velocities. The distributions of residual ions and velocities were presented in figures 4.2, 4.5, 4.7, 4.9,
4.11, and 4.14 for three key cases. These results are essential for the design and handling of the Super-
FRS, to control the radiation damage and to avoid the quenching of the magnets. Successively, the results
have been worked out to release information on the distribution of magnetic rigidities and trajectories of
the ions. This information is useful for the design of the shielding around the Super-FRS. In this section
we want to comment on the latter results.
In figure 4.16-left we present the distribution of the magnetic rigidities for the three cases analysed.
The three vertical lines give the intensity of the surviving primary beams. The horizontal dashed line
represents the intensity available at the actual GSI facility for a 238U primary beam. Please note that the
staggering of the curves is not due to statistical fluctuations. Specifically the peaks close to the magnetic
rigidities of the beams are due to the most produced isotopes (236,237U, 44-47Ca, 41-47K). On the right side of
the figure the corresponding distributions of the radii of the trajectories, when the magnetic field is tuned
in order to transmit the selected fragments, are presented. The magnetic rigidities of the selected fragments
are around 16.8 Tm (for 238U on Ta), 26.6 Tm (for 48Ca on C) and 14.5 Tm (for 238U on C). In tables 4.2,
4.4, 4.6 we collected the results for all the other possible tuning of the magnet. In correspondence to these
tunings the distributions of the radii shift, as shown in figure 4.17. Figure 4.18 collects all the distributions
for the three key cases.
Combining the results we come to the conclusions that intensities above 1010 are expectable in the
region delimited by trajectories with radii between 7.2 m and 19.3 m. In particular, between 8 m and 19.3
54
m intensities around 7 1011 have to be expected. Therefore the region around the 1st dipole of the Super-
FRS will be highly radioactive and adequate shielding have to be considered for the zone delimited by the
circles of radii 7.2 m and 19.3 m.
Figure 4.16: Left: Distributions of the magnetic rigidities for the cases presented in the previous section: 1.5 A GeV 48Ca on C (blue), 1.5 A GeV 238U on C (red), 1.5 A GeV 238U on Ta (black). Right: Corresponding distributions of the radii of the trajectories, when the magnetic field is tuned in order to transmit the selected fragments (11Li, 100Sn, 130Sn, respectively).The 5-cm step in the unit of the y axis is due to the width of the channel of the x axis of figures 4.3, 4.8, 4.12, 4.6, 4.10, 4.15.
Figure 4.17: Left: Distributions of the radii of the trajectories for the residues of 1.5 A GeV 238U on Ta, when the magnet is tuned to 12.03 Tm (curve on the right) and to 21.92 Tm (curve on the left). See table 4.2. Centre: Distributions of the radii of the trajectories for the residues of 1.5 A GeV 48Ca on C, when the magnet is tuned to 11.13 Tm (curve on the right) and to 23.57 Tm (curve on the left). See table 4.4. Right: Distributions of the radii of the trajectories for the residues of 1.5 A GeV 238U on C, when the magnet is tuned to 12.65 Tm (curve on the right) and to 19.84 Tm (curve on the left). See table 4.6. The 5-cm step in the unit of the y axis is due to the width of the channel of the x axis of the θ-Bρ scatter-plot spectra.
55
Figure 4.18: All the distributions of the radii of the trajectories for the residues of 1.5 A GeV 238U on Ta, of 1.5 A GeV 48Ca on C, and of 1.5 A GeV 238U on C. The 5-cm step in the unit of the y axis is due to the width of the channel of the x axis of the θ-Bρ scatter-plot spectra.
Presentation of the numerical results
All the numerical results are gathered in the following tables. They are based on the cross sections
evaluated with a computational tool. The reliability of the code used in this work is rather good for the
evaluation of cross sections of nuclides close to the projectile (in the order of 20% relative error for a
specific isotope) but it gets worse as the mass of the residue decreases. For nuclides far from the projectile
it can be off by a factor of two for some specific nuclide. Therefore it is rather difficult to specify the error
of the calculations. However, one must consider that the purpose of this work is to know the order of
magnitude of the produced radioactive particles, especially the heaviest ones, which are the most
dangerous in terms of safety aspects. Moreover, the general overview of the production is rather realistic.
Concerning the presentation of the numbers in the tables, they were automatically generated. So, please
do not assume that the error is on the last digit.
56
TABLE 4.1
Summary of numerical results for the case of a 238U beam on a tantalum target, at 1.5 GeV/nucleon, with a primary-beam intensity of 1·1012 ions/s. The target is 5.225 g/cm2 thick, corresponding to 20% of the range of the projectile. The selected fragment is 130Sn. GENERAL: Percentage of beam performing nuclear reactions = 11.8 % Percentage of beam performing electromagnetic interactions = 8.2 % Total percentage of beam performing reactions = 20.0 % Percentage of interactions that lead to total disintegration of the nucleus = 20.6 % Percentage of interactions that lead to the formation of residues = 79.4 % Among which: 60.0 % fragmentation, 19.4 % fission Initial beam intensity = 1·1012 ions/s Intensity of surviving beam = 8.0·1011 ions/s Intensity of fragments produced in the reactions = 2.79 ·1011 ions/s Intensity of fragments stopped in the quadrupole = 7·106 ions/s SELECTED CASE: Intensity of fragments going in the left iron wall of the dipole (diffuse) = 2.04·1011 ions/s Intensity of fragments going in the right iron wall of the dipole (diffuse) = 2.4·1010 ions/s Intensity of fragments transmitted = 5.1·1010 ions/s Intensity of surviving beam stopped in the slits (one spot) = 8.0·1011 ions/s
57
58
TABLE 4.3
Summary of numerical results for the case of a 48Ca beam on a carbon target, at 1.5 GeV/nucleon, with a primary-beam intensity of 1·1012 ions/s. The target is 6.0 g/cm2 thick, corresponding to about 14% of the range of the projectile. The selected fragment is 11Li.
GENERAL: Percentage of beam performing nuclear reactions = 38.90 % Percentage of beam performing electromagnetic interactions = 0.12 % Total percentage of beam performing reactions = 39.02 % Percentage of interactions that lead to total disintegration of the nucleus = 26.4 % Percentage of interactions that lead to the formation of residues = 73.6 % Among which: 100.0 % fragmentation, 0 % fission Initial beam intensity = 1·1012 ions/s Intensity of surviving beam = 6.10 ·1011 ions/s Intensity of fragments produced in the reactions = 2.87 ·1011 ions/s Intensity of fragments stopped in the quadrupole = 4.1 ·108 ions/s SELECTED CASE: Intensity of fragments going in the left iron wall of the dipole (diffuse) = 2.866·1011 ions/s Intensity of fragments going in the right iron wall of the dipole (diffuse) = 3·106 ions/s Intensity of fragments transmitted = 7·106 ions/s Intensity of surviving beam stopped the left wall of the dipole (one spot) = 6.10·1011 ions/s
59
60
TABLE 4.5
Summary of numerical results for the case of a 238U beam on a carbon target, at 1.5 GeV/nucleon, with a primary-beam intensity of 1·1012 ions/s. The target is 4.0 g/cm2 thick, corresponding to about 10% of the range of the projectile. The selected fragment is 100Sn.
GENERAL: Percentage of beam performing nuclear reactions = 51.90 % Percentage of beam performing electromagnetic interactions = 0.75 % Total percentage of beam performing reactions = 52.65 % Percentage of interactions that lead to total disintegration of the nucleus = 0.01 % Percentage of interactions that lead to the formation of residues = 99.9 % Among which: 57.7 % fragmentation, 42.3 % fission Initial beam intensity = 1·1012 ions/s Intensity of surviving beam = 4.73 ·1011 ions/s Intensity of fragments produced in the reactions = 7.27 ·1011 ions/s Intensity of fragments stopped in the quadrupole = 4.6 ·108 ions/s SELECTED CASE: Intensity of fragments going in the left iron wall of the dipole (diffuse) = 3.05·1010 ions/s Intensity of fragments going in the right iron wall of the dipole (diffuse) = 5.71·1011 ions/s Intensity of fragments transmitted = 1.25·1011 ions/s Intensity of surviving beam stopped the right wall of the dipole (one spot) = 4.73·1011 ions/s
61
62
Conclusions
The work presented here belongs to a wide series of studies devoted to planning and designing
the future GSI Facility. Specifically, it is related to the problem of the environmental and safety
aspects, connected to the high rate of radioactivity produced.
The essential task of this work was the study of the production of radioactive nuclides in
nucleus-nucleus collisions at relativistic energies. Along with it, the velocity distributions of the
produced nuclides and their propagation through the Super-FRS were investigated. This
knowledge is at the basis of the study of the radiation deposition in the most exposed areas of the
new facility.
The work consisted in determining the yields of the residual nuclides produced in three key
nuclear reactions, their velocity and their trajectories inside the first magnet of the Super-FRS. In
order to do this, the nuclear-reaction Monte-Carlo code ABRABLA, developed in the last years at
GSI [CHA], was opportunely implemented, introducing the description of the kinematics in the
nucleus-nucleus reactions. Along with the ABRABLA code, an analysis program was made to
produce the mapping of the magnetic rigidities and of the angles of the produced nuclides. This
map can be used as input information for detailed ion-optical codes capable to release an exact
and three-dimensional distribution of the residual nuclides around the Super-FRS target area.
The final results showed that the region around the 1st dipole of the Super-FRS will be highly
radioactive: intensities with a peak up to 8·1011 ions/s in one spot are expected in the zone
delimited by the circles of radii 7.2 m and 19.3 m in the first dipole. These ions, and the cascades
of neutrons that they will generate, have to be stopped in devoted shielding structures. The map of
the intensities of the produced residual nuclei has to be used as input information for appropriate
transport codes with which it is possible to determine accurately the cascade of nucleons that
these fluxes of ions will generate and the consequent thickness of the shielding. The surprising
result found in this work – intensities up to 1011 ions/s in the target area of the Super-FRS –
would result in very thick concrete shielding and in rather high construction costs.
63
We like to point out that the maps of the intensities of the produced residual nuclei are of
extreme importance to avoid possible quenching of the superconductiong magnets, and also for
the correct functioning of the magnets. In this context, also the velocity distributions of the
produced ions are of great significance, since the radiation damage depends on the velocity of the
ion.
64
Conclusión
El presente trabajo pertenece a una amplia serie de estudios dedicados a la planificación y
diseño de la futura instalación del GSI. Está relacionado específicamente con los problemas
ambientales y de seguridad, conexos a su vez con el alto nivel de radioactividad producido.
La tarea esencial de este trabajo ha sido el estudio de la producción de núcleos radioactivos en
reacciones núcleo-núcleo a energías relativistas. Además se han investigado las distribuciones de
velocidad de los núcleos producidos y su propagación a través del Super-FRS. Este conocimiento
es la base del estudio sobre la deposición de radiación en el área más expuesta de la nueva
instalación.
Este Trabajo ha consistido en la determinación de la producción de núcleos residuales
generados en tres reacciones nucleares clave, su velocidad y su trayectoria dentro del primer imán
del Super-FRS. Para poder realizar esta tarea, el código Monte Carlo ABRABLA de simulación
de reacciones nucleares, desarrollado en los últimos años en el GSI [CHA], fue oportunamente
implementado introduciendo la descripción de la cinemática de las reacciones núcleo-núcleo.
Además del código ABRABLA, se ha desarrollado un programa de análisis para realizar un mapa
de la rigidez magnética y de los ángulos de los núcleos producidos. Este mapa puede ser usado
como información inicial para códigos especializados de óptica iónica capaces de calcular
ribución exacta y tridimensional de los núcleos residuales alrededor del área de la probeta del
Super-FRS.
Los resultados han mostrado que la región alrededor del primer dipolo del Super-FRS será
altamente radioactiva: Se esperan en un punto de la zona delimitada por los círculos de radios 7.2
m y 19.3 m intensidades con un pico de hasta 8·1011 iones/s. Estos iones y las cascadas de
neutrones que generarán, tienen que ser paradas en estructuras blindantes especificas. El mapa de
las intensidades de los núcleos residuales producidos tiene que ser usado como información
inicial para códigos de transporte apropiados con los que es posible determinar con precisión la
cascada de nucleones que estos flujos de iones generarán, y el consecuente espesor del blindaje.
El sorprendente resultado encontrado en este trabajo – intensidades de hasta 1011 iones/s en el
65
área de la probeta del Super-FRS – resultaría en blindajes muy espesos y en consecuencia costes
de construcción bastante altos.
Es importante subrayar que los mapas de las intensidades de los núcleos residuales producidos
son de extrema importancia para evitar posibles quenching de los imanes superconductores, y
también para asegurar el correcto funcionamiento de los imanes. Asimismo, también las
distribuciones de velocidad de los iones producidos son muy importantes, dado que el daño
producido por la radiación depende de la velocidad del ión.
66
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